{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_coVqVyXuGSV"
   },
   "source": [
    "# Causal Inference Between Two Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "35DGmFTfuGSY"
   },
   "source": [
    "## Setup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "3vxcDrCCuGSZ"
   },
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import numpy.random as rnd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "from abc import abstractmethod\n",
    "from matplotlib.ticker import NullFormatter, NullLocator, MultipleLocator\n",
    "%matplotlib inline\n",
    "from sklearn.svm import SVR\n",
    "from hyppo.independence import Hsic"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5SsyJ0ypuGSf"
   },
   "source": [
    "## Causal Data Generation, Visualization, and Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-YB80qml-QrB"
   },
   "source": [
    "### Data Generator\n",
    "\n",
    "\n",
    "The ```noise``` function generates noise variable according to ```dist``` distribution. Moreover, the ```get_data``` function simulates $Y = f(X) + N_Y$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "K0VuxjfluGSg"
   },
   "outputs": [],
   "source": [
    "def noise(size, dist, val, df = 1):\n",
    "    if dist == 'normal':\n",
    "        return rnd.normal(size = size)\n",
    "    if dist == 'uniform':\n",
    "        return rnd.uniform(0, 1, size = size)\n",
    "    if dist == 't dist':\n",
    "        return rnd.standard_t(df = df, size = size)\n",
    "    if dist == 'interventional':\n",
    "        return np.full(size, val)\n",
    "    \n",
    "def get_data(size, dist_Nx, dist_Ny, f, val_x = None, val_y = None, df = 1):\n",
    "    X = noise(size, dist_Nx, val_x, df)\n",
    "    Ny = noise(size, dist_Ny, val_y, df)\n",
    "    Y = f(X) + Ny\n",
    "    return X, Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "id": "nxW7x2rNuGSl"
   },
   "outputs": [],
   "source": [
    "def plot_observational(size, dist_Nx, dist_Ny, f, Ngrid, Xgrid = None, Ygrid = None, df = 1):\n",
    "    x, y = get_data(size, dist_Nx, dist_Ny, f, df = df)\n",
    "\n",
    "    if Xgrid is None:\n",
    "        H, xbins, ybins = np.histogram2d(x, y, Ngrid)\n",
    "    else:\n",
    "        H, xbins, ybins = np.histogram2d(x, y, [Xgrid, Ygrid])\n",
    "        \n",
    "    H /= np.sum(H)\n",
    "\n",
    "    fig = plt.figure(figsize=(12, 8))\n",
    "\n",
    "    ax_Pxy = plt.axes((0, 0.34, 0.27, 0.52))\n",
    "    ax_Px = plt.axes((0, 0.14, 0.27, 0.2))\n",
    "    ax_Py = plt.axes((-0.1, 0.34, 0.1, 0.52))\n",
    "    ax_cb = plt.axes((0.28, 0.34, 0.01, 0.52))\n",
    "    ax_Px_y = [plt.axes((0.45, 0.7, 0.22, 0.16)),\n",
    "           plt.axes((0.45, 0.5, 0.22, 0.16)),\n",
    "           plt.axes((0.45, 0.3, 0.22, 0.16))]\n",
    "    ax_Py_x = [plt.axes((0.75, 0.7, 0.22, 0.16)),\n",
    "           plt.axes((0.75, 0.5, 0.22, 0.16)),\n",
    "           plt.axes((0.75, 0.3, 0.22, 0.16))]\n",
    "\n",
    "    ax_Px_y[0].xaxis.set_major_formatter(NullFormatter())\n",
    "    ax_Px_y[1].xaxis.set_major_formatter(NullFormatter())\n",
    "    ax_Py_x[0].xaxis.set_major_formatter(NullFormatter())\n",
    "    ax_Py_x[1].xaxis.set_major_formatter(NullFormatter())\n",
    "    ax_Pxy.xaxis.set_major_formatter(NullFormatter())\n",
    "    ax_Pxy.yaxis.set_major_formatter(NullFormatter())\n",
    "    ax_Px.yaxis.set_major_formatter(NullFormatter())\n",
    "    ax_Py.xaxis.set_major_formatter(NullFormatter())\n",
    "\n",
    "    plt.axes(ax_Pxy)\n",
    "    H *= 1000\n",
    "    plt.imshow(H.T, interpolation='nearest', origin='lower', aspect='auto',\n",
    "           cmap=plt.cm.binary)\n",
    "\n",
    "    cb = plt.colorbar(cax=ax_cb)\n",
    "    plt.text(0, 1.02, r'$\\times 10^{-3}$', transform=ax_cb.transAxes)\n",
    "\n",
    "    ax_Px.plot(xbins[1:], H.sum(1), '-k', drawstyle='steps')\n",
    "    ax_Py.plot(H.sum(0), ybins[1:], '-k', drawstyle='steps')\n",
    "\n",
    "    ax_Pxy.set_xlabel('$x$')\n",
    "    ax_Pxy.set_ylabel('$y$')\n",
    "    ax_Px.set_xlabel('$x$')\n",
    "    ax_Px.set_ylabel('$p_X(x)$')\n",
    "    ax_Px.yaxis.set_label_position('right')\n",
    "    ax_Py.set_ylabel('$y$')\n",
    "    ax_Py.set_xlabel('$p_Y(y)$')\n",
    "    ax_Py.xaxis.set_label_position('top')\n",
    "\n",
    "    axis = ax_Pxy.axis()\n",
    "\n",
    "    for i in range(3):\n",
    "        Px_y = H[:, idx[i]] / H[:, idx[i]].sum()\n",
    "        ax_Px_y[i].plot(xbins[1:], Px_y, drawstyle='steps', c=colors[i])\n",
    "\n",
    "        ax_Px_y[i].yaxis.set_major_formatter(NullFormatter())\n",
    "        ax_Px_y[i].set_ylabel('$p_{X|Y}(x | y = %.1f)$' % ybins[idx[i]])\n",
    "    ax_Pxy.axis(axis)\n",
    "    ax_Px_y[2].set_xlabel('$x$')\n",
    "\n",
    "    for i in range(3):\n",
    "        Py_x = H[idx[i]] / H[idx[i]].sum()\n",
    "        ax_Py_x[i].plot(ybins[1:], Py_x, drawstyle='steps', c=colors[i])\n",
    "        ax_Py_x[i].yaxis.set_major_formatter(NullFormatter())\n",
    "        ax_Py_x[i].set_ylabel('$p_{Y|X}(y | x = %.1f)$' % xbins[idx[i]])\n",
    "    ax_Py_x[2].set_xlabel('$y$')\n",
    "\n",
    "    ax_Pxy.set_title('Joint Probability')\n",
    "    ax_Px_y[0].set_title('Conditional Probability')\n",
    "    ax_Py_x[0].set_title('Conditional Probability')\n",
    "\n",
    "    plt.grid(False)\n",
    "    plt.show()\n",
    "    \n",
    "    return xbins, ybins"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "id": "EAO051CNv6k5"
   },
   "outputs": [],
   "source": [
    "def fit(input, target):\n",
    "    svr = SVR(kernel = 'rbf', C = 1000, gamma = 'auto', epsilon = 0.1, coef0 = 1)\n",
    "    svr.fit(input, target)\n",
    "    residual = svr.predict(input) - target\n",
    "    return residual"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "id": "AeTPuAafuGSp"
   },
   "outputs": [],
   "source": [
    "Ngrid = 600\n",
    "n = 10\n",
    "idx = [3 * Ngrid // 4, Ngrid // 2, Ngrid // 4]\n",
    "colors = 'rgb'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-lqb2FUsuGSv"
   },
   "source": [
    "### Model A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3xSxa1WtuGSw"
   },
   "source": [
    "$X := N_X, Y := X^3 + X + N_X$\n",
    "$\\newcommand{\\indep}{\\perp \\!\\!\\! \\perp}$\n",
    "\n",
    "$N_X \\indep N_Y$ \n",
    "\n",
    "$N_X, N_Y \\sim \\mathcal{N}(0, 1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "i_4CO0tSuGSx"
   },
   "source": [
    "##### Observational Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 433
    },
    "id": "1Bx6cpaVuGSy",
    "outputId": "9612debb-b86e-4c5a-e56c-c99716c573d3"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xgrid = np.linspace(-4, 4, Ngrid + 1)\n",
    "Ygrid = np.linspace(-40, 40, Ngrid + 1)\n",
    "xbins, ybins = plot_observational(100000, 'normal', 'normal', lambda x: x**3 + x, Ngrid, Xgrid, Ygrid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uAbU8_ALABIH"
   },
   "source": [
    "As you see in the conditional probablity plots, $P_{X|Y} (x|y)$ depends on different choices of $y$. Hence, the preceding **independence of cause and mechanism** does not apply. As a result, $Y \\rightarrow X$ is not possible."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-QEkmen-uGS2"
   },
   "source": [
    "##### Interventional Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 461
    },
    "id": "fKfp4OmEuGS3",
    "outputId": "dfdc021b-8d58-4ea5-f474-e7f02f1839c6"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_Y^{do(X)}(y)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'interventional', 'normal', lambda x: x**3 + x, val_x = xbins[idx[i]])\n",
    "    sns.distplot(y, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$y$\")\n",
    "    ax[i].set_title(\"$do(X = %.1f)$\" % xbins[idx[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 459
    },
    "id": "IvMgP5_ZuGS7",
    "outputId": "424bd548-8f52-4c7d-e572-938b4e4ad528"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_X^{do(Y)}(x)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'normal', 'interventional', lambda x: 0, val_y = ybins[idx[i]])\n",
    "    sns.distplot(x, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$x$\")\n",
    "    ax[i].set_title(\"$do(Y = %.1f)$\" % ybins[idx[i]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PFQy_kbXDLlJ"
   },
   "source": [
    "Intervention on $Y$ does not change the distribution of $X$, and $P_Y^{do(X=x)}(y) = P_{Y|X}(y|x)$. Consequently, we conclude $X \\rightarrow Y$, which supports our previous inference. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TvQH6GDJyFDP"
   },
   "source": [
    "##### Causal Discovery"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QlmK5XGkHqlQ"
   },
   "source": [
    "Based on the **identifiability of ANMs** theorem, we know that a distribution generically does not admit an ANM in both directions at the same time. The linear Gaussian model is a case that ANM yields in both directions and causal structure learning is impossible. Therefore, our causal learning method, which is checking the independence of residuals, will work in most experiments:\n",
    "\n",
    "\n",
    "\n",
    "1.   We regress $Y$ on $X$, and we write $Y$ as a function $\\hat{f}_Y$ of $X$ plus some noise.\n",
    "2.   We test if $Y - \\hat{f}_Y$ is independent of $Y$. **Note that we use additivity and $X\\perp \\!\\!\\!\\! \\perp N_Y$ assumptions in the both steps.**\n",
    "3.   Then we repeat the procedure with exchanging the roles of $X$ and $Y$.\n",
    "4.   If the independence is accepted for one direction and rejected for the other, we infer the former one as the causal direction.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "av1Nefdav-7z",
    "outputId": "fb02eec8-6f9f-4cda-d27b-d7159bc6cd0d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 1\n",
      "-> HSIC(x, r_y) p-value = 0.189739422434957\n",
      "-> HSIC(y, r_x) p-value = 3.52181022158098e-05 \n",
      "\n",
      "Step 2\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 8.721778832296844e-05 \n",
      "\n",
      "Step 3\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 9.597353342404663e-06 \n",
      "\n",
      "Step 4\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.0002964726335130215 \n",
      "\n",
      "Step 5\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 1.0660657564197857e-05 \n",
      "\n",
      "Step 6\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.0013898528760608179 \n",
      "\n",
      "Step 7\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 1.5921954167442695e-05 \n",
      "\n",
      "Step 8\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 1.7936860835732178e-06 \n",
      "\n",
      "Step 9\n",
      "-> HSIC(x, r_y) p-value = 0.5534269836385153\n",
      "-> HSIC(y, r_x) p-value = 0.00018725476992320107 \n",
      "\n",
      "Step 10\n",
      "-> HSIC(x, r_y) p-value = 0.9071330859478361\n",
      "-> HSIC(y, r_x) p-value = 7.265762379420202e-05 \n",
      "\n",
      "HSIC(x, r_y) p-value average =  0.8650299492021309\n",
      "HSIC(y, r_x) p-value average =  0.00021066474449876388\n"
     ]
    }
   ],
   "source": [
    "p_x = []\n",
    "p_y = []\n",
    "\n",
    "for i in range(10):\n",
    "    print('Step', i+1)\n",
    "\n",
    "    x, y = get_data(200, 'normal', 'normal', lambda x: x**3 + x)\n",
    "    r_y = fit(np.expand_dims(x, axis=1), y)\n",
    "    r_x = fit(np.expand_dims(y, axis=1), x)\n",
    "    p_x.append(Hsic().test(x, r_y, workers = -1)[1])\n",
    "    p_y.append(Hsic().test(y, r_x, workers = -1)[1])\n",
    "\n",
    "    print('-> HSIC(x, r_y) p-value =', p_x[-1])\n",
    "    print('-> HSIC(y, r_x) p-value =', p_y[-1], '\\n')\n",
    "\n",
    "print('HSIC(x, r_y) p-value average = ', sum(p_x) / len(p_x))\n",
    "print('HSIC(y, r_x) p-value average = ', sum(p_y) / len(p_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "gxdFW1UpULm0"
   },
   "source": [
    "Anti-Causal: $Y \\rightarrow X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "_UbctFgLuGTA"
   },
   "source": [
    "### Model B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "D5a3ADSAuGTB"
   },
   "source": [
    "$X := N_X, Y := X + N_X$\n",
    "$\\newcommand{\\indep}{\\perp \\!\\!\\! \\perp}$\n",
    "\n",
    "$N_X \\indep N_Y$ "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fOzF7BHtuGTB"
   },
   "source": [
    "$N_X\\sim \\mathcal{N}(0, 1),\\ N_Y \\sim U(0, 1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "xc544_H7uGTC"
   },
   "source": [
    "##### Observational Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 435
    },
    "id": "eY3ZVCdpuGTC",
    "outputId": "aab18089-6201-4643-a50b-723694aaa367"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xgrid = np.linspace(-4, 4, Ngrid + 1)\n",
    "Ygrid = np.linspace(-8, 8, Ngrid + 1)\n",
    "xbins, ybins = plot_observational(100000, 'normal', 'uniform', lambda x: x, Ngrid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UQ-_bEpkuGTG"
   },
   "source": [
    "##### Interventional Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 463
    },
    "id": "QqbY1uTMuGTH",
    "outputId": "f362f78b-1f22-4971-8893-9c1bd8318058"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_Y^{do(X)}(y)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'interventional', 'uniform', lambda x: x, val_x = xbins[idx[i]])\n",
    "    sns.distplot(y, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$y$\")\n",
    "    ax[i].set_title(\"$do(X = %.1f)$\" % xbins[idx[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 459
    },
    "id": "7nyMbCAhuGTK",
    "outputId": "4ffe5dc7-0b17-458a-f41d-8f9f73d059e8"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_X^{do(Y)}(x)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'normal', 'interventional', lambda x: 0, val_y = ybins[idx[i]])\n",
    "    sns.distplot(x, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$x$\")\n",
    "    ax[i].set_title(\"$do(Y = %.1f)$\" % ybins[idx[i]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "SXLBbDIsgicV"
   },
   "source": [
    "Intervention on $Y$ does not change the distribution of $X$, and $P_Y^{do(X=x)}(y) = P_{Y|X}(y|x)$. Consequently, we conclude $X \\rightarrow Y$, which supports our previous inference. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pq2DJhm_y09Q"
   },
   "source": [
    "##### Causal Discovery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "VY-9Hvliy09V",
    "outputId": "e4769faf-cced-4c55-d8d0-a5833a61030e"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 1\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.4015398231803675 \n",
      "\n",
      "Step 2\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.15771423690796926 \n",
      "\n",
      "Step 3\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.3287326055385955 \n",
      "\n",
      "Step 4\n",
      "-> HSIC(x, r_y) p-value = 0.5800511187427757\n",
      "-> HSIC(y, r_x) p-value = 1.0 \n",
      "\n",
      "Step 5\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.3224162766671361 \n",
      "\n",
      "Step 6\n",
      "-> HSIC(x, r_y) p-value = 0.7447191770872792\n",
      "-> HSIC(y, r_x) p-value = 0.2027408246582995 \n",
      "\n",
      "Step 7\n",
      "-> HSIC(x, r_y) p-value = 0.26074721129111883\n",
      "-> HSIC(y, r_x) p-value = 0.43801181014143176 \n",
      "\n",
      "Step 8\n",
      "-> HSIC(x, r_y) p-value = 0.47736205665901144\n",
      "-> HSIC(y, r_x) p-value = 1.0 \n",
      "\n",
      "Step 9\n",
      "-> HSIC(x, r_y) p-value = 0.8305170280272289\n",
      "-> HSIC(y, r_x) p-value = 0.37507017340856585 \n",
      "\n",
      "Step 10\n",
      "-> HSIC(x, r_y) p-value = 0.30069425156590557\n",
      "-> HSIC(y, r_x) p-value = 0.06088202147788547 \n",
      "\n",
      "HSIC(x, r_y) p-value average =  0.719409084337332\n",
      "HSIC(y, r_x) p-value average =  0.4287107771980251\n"
     ]
    }
   ],
   "source": [
    "p_x = []\n",
    "p_y = []\n",
    "\n",
    "for i in range(10):\n",
    "    print('Step', i+1)\n",
    "\n",
    "    x, y = get_data(200, 'normal', 'uniform', lambda x: x)\n",
    "    r_y = fit(np.expand_dims(x, axis=1), y)\n",
    "    r_x = fit(np.expand_dims(y, axis=1), x)\n",
    "    p_x.append(Hsic().test(x, r_y, workers = -1)[1])\n",
    "    p_y.append(Hsic().test(y, r_x, workers = -1)[1])\n",
    "\n",
    "    print('-> HSIC(x, r_y) p-value =', p_x[-1])\n",
    "    print('-> HSIC(y, r_x) p-value =', p_y[-1], '\\n')\n",
    "\n",
    "print('HSIC(x, r_y) p-value average = ', sum(p_x) / len(p_x))\n",
    "print('HSIC(y, r_x) p-value average = ', sum(p_y) / len(p_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-DEgCJf-UojC"
   },
   "source": [
    "Anti-Causal: $Y \\rightarrow X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-roln_MouGTM"
   },
   "source": [
    "$N_X\\sim U(0, 1),\\ N_Y \\sim \\mathcal{N}(0, 1)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3JGBjHi2uGTN"
   },
   "source": [
    "##### Observational Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 436
    },
    "id": "kYtlVFneuGTN",
    "outputId": "89eb09de-1c65-4b7e-ee5c-955db69500d9"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xgrid = np.linspace(-4, 4, Ngrid + 1)\n",
    "Ygrid = np.linspace(-8, 8, Ngrid + 1)\n",
    "xbins, ybins = plot_observational(100000, 'uniform', 'normal', lambda x: x, Ngrid)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ozk7sHLFuGTS"
   },
   "source": [
    "##### Interventional Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "yvmCPEs-uGTT",
    "outputId": "9ad47b40-4944-46f2-ac32-c4877a6e9276"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Mohammad Reza\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_Y^{do(X)}(y)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'interventional', 'normal', lambda x: x, val_x = xbins[idx[i]])\n",
    "    sns.distplot(y, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$y$\")\n",
    "    ax[i].set_title(\"$do(X = %.1f)$\" % xbins[idx[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "0sIX1jFVuGTW",
    "outputId": "1b4b47f2-7b6e-445a-effa-535ce00f4619",
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Mohammad Reza\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_X^{do(Y)}(x)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'uniform', 'interventional', lambda x: 0, val_y = ybins[idx[i]])\n",
    "    sns.distplot(x, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$x$\")\n",
    "    ax[i].set_title(\"$do(Y = %.1f)$\" % ybins[idx[i]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3Xg1pC75glpc"
   },
   "source": [
    "Intervention on $Y$ does not change the distribution of $X$, and $P_Y^{do(X=x)}(y) = P_{Y|X}(y|x)$. Consequently, we conclude $X \\rightarrow Y$, which supports our previous inference. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-BSVPLX43h3k"
   },
   "source": [
    "##### Causal Discovery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BV7pbclU3lM2",
    "outputId": "080165d8-9d5a-473a-8d90-1ac61f747f1b"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 1\n",
      "-> HSIC(x, r_y) p-value = 0.5402189227383909\n",
      "-> HSIC(y, r_x) p-value = 0.3238099352800575 \n",
      "\n",
      "Step 2\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.07694589662090712 \n",
      "\n",
      "Step 3\n",
      "-> HSIC(x, r_y) p-value = 0.17022899937291808\n",
      "-> HSIC(y, r_x) p-value = 0.0617460854394687 \n",
      "\n",
      "Step 4\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.09510470285120518 \n",
      "\n",
      "Step 5\n",
      "-> HSIC(x, r_y) p-value = 0.16349483977827328\n",
      "-> HSIC(y, r_x) p-value = 0.26169586985258236 \n",
      "\n",
      "Step 6\n",
      "-> HSIC(x, r_y) p-value = 0.4030024134498552\n",
      "-> HSIC(y, r_x) p-value = 0.6063218411755286 \n",
      "\n",
      "Step 7\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.4781181528899502 \n",
      "\n",
      "Step 8\n",
      "-> HSIC(x, r_y) p-value = 0.3454141060338366\n",
      "-> HSIC(y, r_x) p-value = 0.08711277504500683 \n",
      "\n",
      "Step 9\n",
      "-> HSIC(x, r_y) p-value = 0.4638634717441005\n",
      "-> HSIC(y, r_x) p-value = 0.07038918339814569 \n",
      "\n",
      "Step 10\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.031153933946466424 \n",
      "\n",
      "HSIC(x, r_y) p-value average =  0.6086222753117374\n",
      "HSIC(y, r_x) p-value average =  0.2092398376499319\n"
     ]
    }
   ],
   "source": [
    "p_x = []\n",
    "p_y = []\n",
    "\n",
    "for i in range(10):\n",
    "    print('Step', i+1)\n",
    "\n",
    "    x, y = get_data(200, 'uniform', 'normal', lambda x: x)\n",
    "    r_y = fit(np.expand_dims(x, axis=1), y)\n",
    "    r_x = fit(np.expand_dims(y, axis=1), x)\n",
    "    p_x.append(Hsic().test(x, r_y, workers = -1)[1])\n",
    "    p_y.append(Hsic().test(y, r_x, workers = -1)[1])\n",
    "\n",
    "    print('-> HSIC(x, r_y) p-value =', p_x[-1])\n",
    "    print('-> HSIC(y, r_x) p-value =', p_y[-1], '\\n')\n",
    "\n",
    "print('HSIC(x, r_y) p-value average = ', sum(p_x) / len(p_x))\n",
    "print('HSIC(y, r_x) p-value average = ', sum(p_y) / len(p_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "e0v-mweGViAc"
   },
   "source": [
    "Anti-Causal: $Y \\rightarrow X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "RCrl9wNIuGTa"
   },
   "source": [
    "$N_X\\sim \\mathcal{N}(0, 1),\\ N_Y \\sim$ Student's t-Distribution with degree of freedom $= 1$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HEl2bfwbuGTa"
   },
   "source": [
    "##### Observational Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "UKsNUp1RuGTb",
    "outputId": "fbcb1868-8d8a-469c-d79a-fc06d7fde4ec"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Mohammad Reza\\Anaconda3\\lib\\site-packages\\matplotlib\\cbook\\deprecation.py:107: MatplotlibDeprecationWarning: Using pyplot.axes(ax) with ax an Axes argument is deprecated. Please use pyplot.sca(ax) instead.\n",
      "  warnings.warn(message, mplDeprecation, stacklevel=1)\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 10 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xgrid = np.linspace(-4, 4, Ngrid + 1)\n",
    "Ygrid = np.linspace(-10, 10, Ngrid + 1)\n",
    "xbins, ybins = plot_observational(100000, 'normal', 't dist', lambda x: x, Ngrid, Xgrid, Ygrid, df = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-08qjlOJuGTd"
   },
   "source": [
    "##### Interventional Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "UDle-yLpuGTe",
    "outputId": "d59d4563-554d-42b1-9be5-8c0f9a2dd6ed"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Mohammad Reza\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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Z0+jWZvWTpwPLIuLPgJuqtltOpExC5L9iTXBZFElSg2bxOpzSpHl7proMc5bagc+c1qvNavs6ei9M/KGpnLd2kxlOSVKDHFIr9dd+ezYyMtxz0cwyzCG1mq0MOCVJDTLglPrz9kx1MeBU8+zRJEkNms3rcEqT5e2Z6mLAqeZZJCBJapDrcEr9eXumuhhwqnk+QpMkNcghtVJ/3p6pLgacap49miSpQQacUn/enqkuBpxqnj2aJKlBBpxSf96eqS4GnGqeRQKSpAa11uHcNuqkQVIv3p6pLgacap6P0CRJDTLDKfXn7ZnqYsCp5tmjSZIaZMAp9eftmepiwKnm2aNJkhrksihSf96eqS4GnGqeRQKSpAa1MpzbdljDKfXi7ZnqYsCp5vkITZLUIIfUSv15e6a6GHCqefZokqQGGXBK/Xl7proYcKp59miSpAa1lkUx4JR68/ZMdTHgVPMsEpAkNWhnDafrcEo9eXumuhhwqnk+QpMkNcghtVJ/3p6pLgacap49miSpQQacUn/enqkuBpxqnj2aJKlBrsMp9eftmepiwKnmWSQgSWqQ63BK/Xl7proYcKp5PkKTJDXIIbVSf96eqS4GnGqePZokqUEGnFJ/3p6pLgacap49miSpQa7DKfXn7ZnqYsCp5lkkIElqSLb9t8Z1OKXevD1TXQw41TwfoUmSGtIaTgtmOKWJeHumuhhwqnn2aJKkhhhwSpPTymx6e6ZBG2rAGRHHRMSaiFgbEWd0+X6viLi0+v76iDik7bszq+1rIuLofm1GxKFVG7dXbe7Z9t3bI2J1RKyKiH+o74oFGHBKkhrTqt8EA06pl/ZhtA6p1aANLeCMiBHgPOBYYCFwYkQs7NjtZGBjZh4GnAucUx27EFgCHA4cA5wfESN92jwHODczFwAbq7aJiAXAmcAvZubhwHtrumS1WCQgSWpIe4bTGk6pu/YcgPkADdowM5xHAGszc11mPgEsAxZ37LMYuLh6vxw4KiKi2r4sM7dm5p3A2qq9rm1WxxxZtUHV5vHV+/8OnJeZGwEy84EarlXtzHBKkhrikFqpPwNO1WmYAecBwD1tn9dX27ruk5nbgc3AvAmO7bV9HrCpaqPzt14MvDgivhUR10XEMbt5XerHgFOS1BADTqk/A07Vae4Qfzu6bOscY9lrn17buwXQE+0P5Z/BAuANwIHANyPiZZm5adyJRCwFlgIcfPDBXZrTpFmVLklqSPuyKAacUnfWcKpOw8xwrgcOavt8IHBvr30iYi6wL/DQBMf22v4gsF/VRudvrQcuz8xt1fDcNZQAdJzMvCAzF2Xmovnz50/xUjVOK9C0R5Mk1cwMp9SfGU7VaZgB543Agmr22D0pkwCt6NhnBXBS9f4E4BtZHlWuAJZUs9geSgkQb+jVZnXM1VUbVG1eXr3/MvCfACJif8oQ23UDv1qNcUitpqkmZ9Zu+/7jEfFIXdckzXTjJg3a4aRBUjcGnKrT0ALOqp7yVOAq4DbgssxcFRFnRcRx1W4XAvMiYi1wGnBGdewq4DJgNXAlcEpm7ujVZtXW6cBpVVvzqrap9v1JRKymBKXvy8yf1Hnts54Bp6ahIcysTUQsAvar9cKkGc5lUaT+DDhVp2HWcJKZVwBXdGz7QNv7x4G39Tj2bODsybRZbV9HmcW2c3tSgtnTpnj6erKs4dT0tHMWbICIaM2svbptn8XAh6r3y4FPdM6sDdxZPfhq9Udd26yC0b8AfgP41TovTJrJHFIr9WcNp+o0zCG1mq2s4dT01OTM2lBGa6zIzPsmOqmIWBoRKyNi5YYNG6Z0QdJsMNsDzjpKAarvRiLipoj4Sv1XobqZ4VSdDDjVPIfUanqqY2btrtsj4gWU0R0f73dSTmgmTWxcDefo7KrhrKMUoO2436WUL2kGMOBUnQw41TwDTk1PTc6s/SrgMGBtRNwFPKMahitpimb5sig7SwEy8wmgNWy/3WLg4ur9cuCozlKAahb/naUAEXEg8Bbg7xq4BjXAgFN1MuBU86zh1PTU5Mza/5iZz8vMQzLzEGBLlX2QNEWzfEhtHaUAAH8F/CHgf8hnCGs4VaehThqkWcoaTk1Dmbk9IlqzYI8AF7Vm1gZWZuYKyuzXl1TZyIcoASTVfq2ZtbdTzawN0K3Npq9NmslmecA58FKAiPjPwAOZ+Z2IeMOEPx6xFFgKcPDBB/c/Ww2NGU7VyYBTzXNIraapJmfW7thn7ydzvpLGAs69RvaajetwTqUUYP0kSwGOA46LiF8BngbsExF/n5m/2fnjmXkBcAHAokWLfMr8FGbAqTo5pFbNM+CUJDWktQ7nHiN7zMYM58BLATLzzMw8sBruv6Taf5dgU9OLAafqZIZTzbOGU5LUkFaGc8+RPWddhrOuUgDNPNZwqk4GnGqeNZySpIa0D6l9bNtjQz6b5tVRCtD2/TXANYM4Tw2XGU7VySG1ap5DaiVJDRmX4Zxl63BKk2XAqToZcKp5BpySpIa01uFs1XCmo2ukXRhwqk4GnGqeNZySpIa0ZzjbP0saYw2n6mTAqeZZwylJakh7DSfMyrU4pb7McKpOBpxqnkNqJUkN6cxwWscp7cqAU3Uy4FTzDDglSQ1pX4cTzHBK3Rhwqk4GnGpeayitQ2olSTXrzHAacEq7soZTdTLgVPPMcEqSGmINp9SfGU7VyYBTzTPglCQ1pLUMys4azh3WcEqdDDhVJwNONc+AU5LUkFaG0xpOqTcDTtXJgFPNs4ZTktQQazil/qzhVJ0MONU8M5ySpIZYwyn1Z4ZTdTLgVPMMOCVJDdm5LMoch9RKvRhwqk4GnGqeAackqSGdQ2q3jTppkNTJgFN1MuBU86zhlCQ1xBpOqT9rOFUnA041zwynJKkhO2s451rDKfVihlN1GmrAGRHHRMSaiFgbEWd0+X6viLi0+v76iDik7bszq+1rIuLofm1GxKFVG7dXbe5ZbX9nRGyIiJurv3fVe9Uy4JQkNaW1Dqc1nFJvBpyq09ACzogYAc4DjgUWAidGxMKO3U4GNmbmYcC5wDnVsQuBJcDhwDHA+REx0qfNc4BzM3MBsLFqu+XSzHxl9fd3NVyu2hlwSpIasksN5w5rOKVODqlVnYaZ4TwCWJuZ6zLzCWAZsLhjn8XAxdX75cBRERHV9mWZuTUz7wTWVu11bbM65siqDao2j6/x2jQRazglSQ2xhlPqzwyn6jTMgPMA4J62z+urbV33ycztwGZg3gTH9to+D9hUtdHtt94aEbdExPKIOGh3LkqTYIZTktQQazil/gw4VadhBpzRZVtnyqvXPoPaDvD/gEMy8+eArzOWUR1/IhFLI2JlRKzcsGFDt100WQackqSGuA6n1J8Bp+o0zIBzPdCeTTwQuLfXPhExF9gXeGiCY3ttfxDYr2pj3G9l5k8yc2u1/W+BV3c72cy8IDMXZeai+fPnT+EytQsDTklSQ1yHU+rPGk7VaZgB543Agmr22D0pkwCt6NhnBXBS9f4E4BtZpptbASypZrE9FFgA3NCrzeqYq6s2qNq8HCAint/2e8cBtw34OtXJGk5JUkOs4ZT6M8OpOs3tv0s9MnN7RJwKXAWMABdl5qqIOAtYmZkrgAuBSyJiLSWzuaQ6dlVEXAasBrYDp2TmDoBubVY/eTqwLCL+DLipahvgdyLiuKqdh4B31nzpMsMpSWqINZxSfwacqtPQAk6AzLwCuKJj2wfa3j8OvK3HsWcDZ0+mzWr7Osostp3bzwTOnOq5azcYcEqSGuI6nFJ/Bpyq0zCH1Gq2ag2ltUeTJNXMdTil/qzhVJ0MONW89kDTXk2SVCNrOKX+zHCqTgacap4BpySpIdZwSv0ZcKpOBpxqnr2aJKkhrsMp9eetmepkwKnmtWc17dUkSTVyHU6pP2s4VScDTjXPIbWSpIZYwyn1Z4ZTdTLgVPPs1SRJDWkti2INp9Sbt2aqkwGnmmevJklqSCvDORIjBGHAKXXhrZnqZMCp5lnDKUlqSCvgnBNzmDtnrutwSl1Yw6k6GXCqedZwSpIa0hlwmuGUdmWGU3Uy4FTz7NUkSQ1pLYsyJ+awx8geBpxSF96aqU5POuCMiGdGxMggT0azhL2aJKkhrQxnRJjhlHrw1kx1mnTAGRFzIuI3IuIfI+IB4PvAfRGxKiL+IiIW1HeamlGs4dQ0FRHHRMSaiFgbEWd0+X6viLi0+v76iDik7bszq+1rIuLofm1GxIUR8d2IuCUilkfE3nVfnzQT7VLD6Tqc0i6s4VSdppLhvBp4EXAm8LzMPCgzfwZ4PXAd8JGI+M0azlEzjTWcmoaqER3nAccCC4ETI2Jhx24nAxsz8zDgXOCc6tiFwBLgcOAY4PyIGOnT5u9l5isy8+eAu4FTa71AaYZqDzhHYoQdozuGfEbSU48ZTtVp7hT2fWNm7vJYMDMfAr4AfCEi9hjYmWnmslfT9HQEsDYz1wFExDJgMbC6bZ/FwIeq98uBT0REVNuXZeZW4M6IWFu1R682M/On1bYAng74dEZ6ElrrcM6JOYzMGWFHGnBKnbw1U50mneFsBZsR8fWIeMVE+0gTslfT9HQAcE/b5/XVtq77ZOZ2YDMwb4JjJ2wzIj4F3A+8BPj4IC5Cmm121nASJcM5ywLOQZcCRMTTIuKGasj/qoj40+auRnXx1kx1ejKTBv0hcG5EfCoinj/oE9IsYA2npqfosq0z69hrn6luL28y/yvwAuA24Ne7nlTE0ohYGRErN2zY0G0XaVYbN6R2zuwaUltHKQCwFTgyM18BvBI4JiJ+oYnrUX2s4VSdphxwZua/Z+aRwFeAKyPigxHx9MGfmmas0VGYW43mtlfT9LEeOKjt84HAvb32iYi5wL7AQxMc27fNzNwBXAq8tdtJZeYFmbkoMxfNnz9/ipckzXy71HDOrgznzlKAzHwCaA3bb7cYuLh6vxw4qrMUIDPvBNYCR2TxSLX/HtWf/zGf5lrP/+fONRegwXtSy6JUHdEa4JPAe4DbI+K3BnlimsHaA057NU0fNwILIuLQiNiT8uR/Rcc+K4CTqvcnAN/IUkC2AlhSDV07FFgA3NCrzSgOg5397X+hzAwuaYpa63BGxKzLcFJPKQDVpGc3Aw8A/5SZ13f7cUdgTB8GnKrTlAPOiLgW+BFl2MUBwDuBNwBHRMQFgzw5zVCjozAyMvZemgaqG7FTgasoQ1wvy8xVEXFWRBxX7XYhMK+aFOg04Izq2FXAZZQJhq4ETsnMHb3apAy1vTgibgVuBZ4PnNXQpUozyizPcNZRCkDVf72SMirjiIh4WbcfdwTG9NG6HRsZ8dZMgzfpWWojIqon9b8NrMrcZSzkeyLiBwM9O81MmQacmpYy8wrgio5tH2h7/zjwth7Hng2cPck2R4FfHMApS7PebK7hZGqlAOsnWQqwU2ZuiohrKDWe3xvomatRrbv6kRGrnTR4U1qHMyLeA/y0PdiMiD0j4siIuBj4yMDPUDOPNZySpIbM8gznwEsBImJ+ROwHUM3h8UYc8j/tOaRWdZrKOpzHAP8N+FzV8WyirA03B/gacG5m3jz4U9SMMzoKe+459l6SpJq0npEHwZyYszMAnQ0yc3tEtIbtjwAXtUoBgJWZuYJSCnBJVQrwECUopdqvVQqwnaoUoFqh4OJqxto5lFKArzR/dRokh9SqTpMOOKuhYudTpsXeA9gfeCwzN9V1cpqhrOGUJDVklg+pHXgpQGbeArxq8GeqYTLgVJ2mUsM5H9gHuDsztwH31XZWmtkynaVWktSIWT6kVpqUVoXT3LlWO2nw+tZwVlNaX0J5wvVu4NMRcX41rHa3RMQxEbEmItZGxBldvt8rIi6tvr8+Ig5p++7MavuaiDi6X5tV/cL1EXF71eaeHb91QkRkRCza3etSH9ZwSpIaMtsznNJkWMOpOk0mw7kyM8ctdxIRzwResDs/XI39Pw94E2UmtBsjYkVmrm7b7WRgY2YeFhFLgHOAX4+IhZQag8Or8/h6RLy4OqZXm+dQ6kyXRcRfV21/sjqXZwG/A3RdR0oD5pBaSVJDxq3DaYZT6sohtarTZGapfVPnhsx8NDNv383fPgJYm5nrMvMJYBmwuGOfxcDF1fvlwFHVIuiLgWWZuTUz7wTWVu11bbNfpZQaAAAgAElEQVQ65siqDao2j2/7nf8FfBR4fDevSZNhwClJakgrwxmEGU6pB5dFUZ0mE3CujYi/qpY/+c2I+MKAfvsA4J62z+urbV33qRZI3wzMm+DYXtvnAZuqNsb9VkS8CjjIGdYaZA2nJKkhozlKEGY4pQk4pFZ1mkzA+SXK0Nt7q9cTBvTb0WVb5zOVXvsMZHtEzAHOBX5/gvMsJ1JqWVdGxMoNGzb0210TsYZTktSQzGROlNsdM5xSdwacqtNkAs7PAV8FfhF4M/DsAf32euCgts8HUoLarvtExFxgX8oaUb2O7bX9QWC/qo327c8CXgZcExF3Ab8ArOg2cVBmXpCZizJz0fz586d8sapklj+H1EqSGjCao5TKGsxwSj20bsfmzPHWTIPXN+DMzF/PzH/MzDXA71HW4hyEG4EF1eyxe1ImAVrRsc8K4KTq/QnAN7Ks4LwCWFLNYnsosAC4oVeb1TFXM5adPQm4PDM3Z+b+mXlIZh4CXAccl5krB3SN6tReJAD2apKkWo3mqBlOqY9MiCgBp4PPNGh9Z6mNiKdViwKTmT+OiJM7tz8Zmbk9Ik4FrgJGgIsyc1VEnEWZGXcFcCFwSUSspWQ2l1THroqIy4DVwHbglMzyyLJbm9VPng4si4g/A26q2lbT2hd6av8sSVINxgWcZjilrkZHS7BphlN1mMyyKB+JiFFKcLcJOLTKKn4W+Nbu/HhmXgFc0bHtA23vHwfe1uPYsylrg/Zts9q+jjKL7UTn84bJnLd2Q3uRQPtnSZJqkFjDKfVjwKk69Q04M/O9EfFs4BXAc4ArM/PW2s9MM1P7Qk/tnyVJqkFrllowwyn10go4I7w10+BNJsMJpXbzpcCjwIfrOx3NeNZwSpIaZA2n1J81nKrTZGapBXh2Zr4NWAr8To3no5muc0itvZokqUbWcEr9OaRWdZpswPlERPxHypqWz6zxfDTTWcMpSWqQ63BK/Rlwqk6TDTjfDxwFXABcVt/paMazhlOS1CDX4ZT6s4ZTdZrMsijvAG7MzL/o8f1bMvMfB35mmpms4ZQkNWiXIbVmOKVdtNdwemumQZvMpEEbgPMjYk/gQeAHmXlG2/cvj4gXZObf1nKGmlms4ZQkNWiXSYPMcEq7aB9Su337sM9GM03fIbWZ+TXg+sz8JeAkYO+O7z8CbIuIcyPi9RGxd7d2JMAaTklSo8atw2mGU+rKGk7VabI1nPtExKuBrXRMGhQR/wM4HvgecATwyYGeoWYWazglSQ0atw6nGU6pK2s4VafJrsN5GvA/gFOAKzu+uz8zjx/oWWnmsoZTktQgazil/lyHU3WaVIYzM7cBm4HjgE9GxGci4lnVd1+q8fw001jDKUlqkDWcUn8OqVWdJjukFuBPgDcBLwF+CPx5LWekmc0aTklSg6zhlPoz4FSdJjukFuCnmXlT9f5PIuL6Ok5IM5w1nJKkBo1bh3POCKPpf3ekTtZwqk5TCTifHxFLgduA7wN71HNKmtGs4ZQkNWiXGk6H1Eq7sIZTdZpKwPlB4OeAdwAvB/aOiCuA7wK3ZObnajg/zTTWcEqSGtQecLZe27dJckit6jXpgDMzL2j/HBEHUgLQlwO/Ahhwqj9rOCVJDcrMccuiAOwY3cGcEQNOqcWAU3WaSoZznMxcD6wHrhjc6WjGs4ZTktSgziG1ADtyB3tYGSTtNDpahtRaw6k6+HhPzbKGU5LUoM5lUQBnqpU6ZI5lOK120qAZcKpZ1nBKkhrUuSwK4MRBUgeH1KpOBpxqlkNqJUkN6lwWBcxwSp1cFkV1MuBUsww4JUkN6lXDKWlMq4bTDKfqYMCpZrWG0DpLrSSpAdZwSv1Zw6k6GXCqWdZwSpIalGkNp9SPNZyqkwGnmuWQWklSg0ZztOs6nJLGWMOpOhlwqlkGnJKkBlnDKfXXXsPp4DMN2lADzog4JiLWRMTaiDijy/d7RcSl1ffXR8Qhbd+dWW1fExFH92szIg6t2ri9anPPavtvR8StEXFzRFwbEQvrvepZzhpOSVKDrOGU+muv4fTWTIM2tIAzIkaA84BjgYXAiV2CvZOBjZl5GHAucE517EJgCXA4cAxwfkSM9GnzHODczFwAbKzaBviHzHx5Zr4S+CjwsVouWIU1nJKkBrkOp9SfNZyq0zAznEcAazNzXWY+ASwDFnfssxi4uHq/HDgqymJai4Flmbk1M+8E1lbtdW2zOubIqg2qNo8HyMyftv3eMwEjoDo5pFaS1CDX4ZT6s4ZTdRpmwHkAcE/b5/XVtq77ZOZ2YDMwb4Jje22fB2yq2tjltyLilIi4g5Lh/J3duipNzIBT01jDZQCfrbZ/LyIuiog96r4+aSayhlPqL9MaTtVnmAFndNnW+X/xXvsMant5k3leZr4IOB34464nG7E0IlZGxMoNGzZ020WTYQ2npqkhlAF8FngJ8HLg6cC7arw8acaa7TWcg35QFhEHRcTVEXFbRKyKiN9t7mpUF4fUqk7DDDjXAwe1fT4QuLfXPhExF9gXeGiCY3ttfxDYr2qj129BGYJ7fLeTzcwLMnNRZi6aP39+34tTD9ZwavpqrAwAIDOvyApwA6XfkjRFs3kdzjoelAHbgd/PzJcCvwCc4oSL058Bp+o0zIDzRmBBNXvsnpRObUXHPiuAk6r3JwDfqG6+VgBLqqdyhwILKDdkXdusjrm6aoOqzcsBImJB2++9Bbh9wNepdg6p1fTVZBnATtVQ2t8CrtztK5BmoVm+DufAH5Rl5n2Z+e8AmfkwcBu79oWaZqzhVJ3m9t+lHpm5PSJOBa4CRoCLMnNVRJwFrMzMFcCFwCURsZaS2VxSHbsqIi4DVlOetJ2SWR5Xdmuz+snTgWUR8WfATVXbAKdGxBuBbZTZa1sBrupgwKnpq44ygG4P/TrbPB/418z8ZteTilgKLAU4+OCDu+0izWqzvIaz20Ot1/Tap7o3a39Qdl3HsZ0PxA4BXgVcP8iTVvOs4VSdhhZwQhkyBlzRse0Dbe8fB97W49izgbMn02a1fR3lSV/ndmsPmmQNp6avqZQBrJ9kGQATtRkRHwTmA+/udVKZeQFwAcCiRYu8TZA6zPIazjoelJWDIvYGvgC8t2PGf9r28YHYNOGQWtVpmENqNRtZw6npq7EyAICIeBdwNHBiZvqff+lJmuXrcNYxX0ZrqP8XgM9m5hd7/bjzX0wfBpyqkwGnmuWQWk1TVU1ma8j+bcBlrTKAiDiu2u1CYF5VBnAacEZ17CqgVQZwJVUZQK82q7b+Gngu8O2IuDkido7+kDR5s3wdzoE/KKvqOy8EbsvMjzVyFaqdNZyq01CH1GoWMuDUNNZwGYD9szQA3Wo4R2fJoIE65suIiNdRJjK7NSJurn7qj6q+TNOUNZyqkzc0apY1nJKkBnWt4Zw9Q2oH/qAsM6+le32npjGH1KpODqlVs6zhlCQ1qOs6nLNnSK00KQacqpMBp5rlkFpJUoO6rsM5izKc0mRYw6k6GXCqWa2MpgGnJKkBXdfhNMMpjWMNp+pkwKlmmeGUJDWofVmU1qsZTmm89iG1mQadGiwDTjWrFWC292qSJNWk66RBZjilcdoDTvD2TINlwKlmtQLOCAsFJEm1G7cOZ1jDKXXTXsPZ+iwNigGnmtV6ZOZUaJKkBpjhlPprr+FsfZYGxYBTzeocUmvAKUmqUddlUcxwSuN0Dqn19kyDZMCpZlnDKUlqUNdlUcxwSuMYcKpOBpxqljWckqQGdV0WxQynNI41nKqTAaeaZQ2nJKlB1nBK/VnDqToZcKpZDqmVJDWofR1OM5xSdw6pVZ0MONUsh9RKkhpkDafUn0NqVScDTjXLWWolSQ2yhlPqzwyn6mTAqWZZwylJapA1nFJ/1nCqTgacapY1nJKkBrkOp9SfGU7VyYBTzbKGU5LUoNEcJcIaTmki1nCqTgacapY1nJKkBlnDKfVnhlN1MuBUs6zhlCQ1yBpOqT9rOFUnA041yxpOSVKD2tfhbL2a4ZTGM8OpOhlwqlnWcEqSGtS+DieUYbVmOKXxrOFUnYYacEbEMRGxJiLWRsQZXb7fKyIurb6/PiIOafvuzGr7mog4ul+bEXFo1cbtVZt7VttPi4jVEXFLRPxzRLyw3que5azhlCQ1qH1ILZRhtWY4pfE6M5wOQNMgDS3gjIgR4DzgWGAhcGJELOzY7WRgY2YeBpwLnFMduxBYAhwOHAOcHxEjfdo8Bzg3MxcAG6u2AW4CFmXmzwHLgY/Wcb2qWMMpSWpQ+7IoUDKco+l/e6R2nTWc3p5pkIaZ4TwCWJuZ6zLzCWAZsLhjn8XAxdX75cBRUeY2Xwwsy8ytmXknsLZqr2ub1TFHVm1QtXk8QGZenZlbqu3XAQfWcK1qsYZTktSgrhlOh9RK41jDqToNM+A8ALin7fP6alvXfTJzO7AZmDfBsb22zwM2VW30+i0oWc+vPolr0WRZwylJalD7OpxQ1XA6pFYaxxpO1WnuEH87umzrTHf12qfX9m4B9ET7j/1QxG8Ci4Bf7rIvEbEUWApw8MEHd9tFk2ENpySpQWY4pf4yreFUfYaZ4VwPHNT2+UDg3l77RMRcYF/goQmO7bX9QWC/qo1dfisi3gi8HzguM7d2O9nMvCAzF2Xmovnz50/hMjWONZySpAa1L4sCZjilbkZHreFUfYYZcN4ILKhmj92TMgnQio59VgAnVe9PAL6RmVltX1LNYnsosAC4oVeb1TFXV21QtXk5QES8CvgbSrD5QE3XqhZrOCVJDTLDKfVnDafqNLQhtZm5PSJOBa4CRoCLMnNVRJwFrMzMFcCFwCURsZaS2VxSHbsqIi4DVgPbgVMyy+PKbm1WP3k6sCwi/owyM+2F1fa/APYGPl/VeNydmcfVfPmzlzWckqQGdV2H0wynNI41nKrTMGs4ycwrgCs6tn2g7f3jwNt6HHs2cPZk2qy2r6PMYtu5/Y1TPnE9edZwSpIaktUomvYM55yYY8ApdbCGU3Ua5pBazUbWcEqSGpLsGnA6pFbalTWcqpMBp5plDackqSGjWf6b46RBUm+Zu2Y4DTg1SAacapY1nJKkhrQCznHrcJrhlMZpH3xmDafqYMCpZrXGbIBDaiVJtTLDKfXXWe3Uvk0aBANONas1ZgMMOCVJteo2aZAZTmm89sFnDqlVHQw41azWvNtgDackqVZmOKX+OqfXaN8mDYIBp5rVPqTWGk5JUo121nBiDafUS3vAaQ2n6mDAqWY5pFaS1BAznFJ/1nCqbgacalbnkFoDTklSTVyHU+rPGk7VzYBTzbKGU9NYRBwTEWsiYm1EnNHl+70i4tLq++sj4pC2786stq+JiKP7tRkRp1bbMiL2r/vapJnIDKfUnzWcqpsBp5plDaemqYgYAc4DjgUWAidGxMKO3U4GNmbmYcC5wDnVsQuBJcDhwDHA+REx0qfNbwFvBH5Y64VJM5jrcNb2oOyiiHggIr7XzFWoTtZwqm4GnGqWNZyavo4A1mbmusx8AlgGLO7YZzFwcfV+OXBUlDvdxcCyzNyamXcCa6v2eraZmTdl5l11X5Q0k832DGcdD8qqYz5dbdMMYA2n6mbAqWZZw6np6wDgnrbP66ttXffJzO3AZmDeBMdOpk1JT5LrcNbyoIzM/FfgoSYuQPWzhlN1M+BUszqH1PoITdNHdNnW+X/gXvtMdfvkTypiaUSsjIiVGzZsmMqh0ozXdVmUWZThpJ4HZZphHFKruhlwqllmODV9rQcOavt8IHBvr30iYi6wLyUL0OvYybQ5ocy8IDMXZeai+fPnT+VQacbrOqR2dmU463hQNvkf94HYtOCkQaqbAaeaZQ2npq8bgQURcWhE7EmpbVrRsc8K4KTq/QnAN7KM6VsBLKkm5zgUWADcMMk2JT1JXZdFmV0ZzjoelE2aD8SmB2s4VTcDTjXLDKemqWqo2anAVcBtwGWZuSoizoqI46rdLgTmRcRa4DTgjOrYVcBlwGrgSuCUzNzRq02AiPidiFhPucm7JSL+rqlrlWaKXhnO1vZZoI4HZZphrOFU3eYO+wQ0y1jDqWksM68ArujY9oG2948Db+tx7NnA2ZNps9r+f4H/u5unLM1qXZdFidkzpDYzt0dE66HWCHBR60EZsDIzV1AelF1SPSh7iBKUUu3XelC2nepBGUBEfA54A7B/9WDsg5l5YcOXpwGxhlN1M+BUs8xwSpIa0rOGc/YMqa3rQdmJAz5NDZE1nKqbQ2rVLGs4JUkN6bosyizKcEqTYQ2n6maGU8249lp48EEznJKkxpjhlPqzhlN1M8OpZvzv/w1nnGENpySpMT3X4TTDKbFjB3z4w7B5c/lsDafqYoZTzXjkEXj0UTOckqTGdM1wzq5lUaSebrkF/uiPug+p9fZMg2SGU8149NHyZw2nJKkhXdfhnGOGU4KSCwB4+OHyag2n6mLAqWY8+ihs2WKGU5LUGDOcUm+PPlpef/rT8moNp+oy1IAzIo6JiDURsTYizujy/V4RcWn1/fURcUjbd2dW29dExNH92qwWPb4+Im6v2tyz2v5LEfHvEbE9Ik6o94pnsS1bYOtW2LbNGk5JUiO6rsNphlMCumc4reFUHYYWcEbECHAecCywEDgxIhZ27HYysDEzDwPOBc6pjl1IWZj4cOAY4PyIGOnT5jnAuZm5ANhYtQ1wN/BO4B/quE5VWo/RHnnEDKckqRHdMpxzYo4ZTonxt2bgkFrVZ5gZziOAtZm5LjOfAJYBizv2WQxcXL1fDhwV5THlYmBZZm7NzDuBtVV7XdusjjmyaoOqzeMBMvOuzLwFMPKpU6tXe/hhA05JUiNch1Pqrf3WDJw0SPUZZsB5AHBP2+f11bau+2TmdmAzMG+CY3ttnwdsqtro9VuqS6YBpySpca7DKfXWGXBaw6m6DDPgjC7bOhP4vfYZ1PZJi4ilEbEyIlZu2LBhKodq69axnuuRR6zhlCQ1wnU4pd66Dam1hlN1GGbAuR44qO3zgcC9vfaJiLnAvsBDExzba/uDwH5VG71+a0KZeUFmLsrMRfPnz5/KodqyZey9NZySpIaY4ZR6m2hIrfkADdIwA84bgQXV7LF7UiYBWtGxzwrgpOr9CcA3shRkrACWVLPYHgosAG7o1WZ1zNVVG1RtXl7jtaldq0cDh9RKkhrTdR1OM5wSsOuyKNZwqi5DCzirespTgauA24DLMnNVRJwVEcdVu10IzIuItcBpwBnVsauAy4DVwJXAKZm5o1ebVVunA6dVbc2r2iYifj4i1gNvA/4mIlr7a1DaA87HHx8fcGbCV74CH/nIcM5NkjQjXbf+OraPlqkbOjOcSe6cUEiarTqXRbGGU3WZ23+X+mTmFcAVHds+0Pb+cUog2O3Ys4GzJ9NmtX0dZRbbzu03UobYqi7tASeMr+EcHYW//3u45ho4Y5elWCVJmrLVG1bz2gtfyx+//o+BjnU4YwSAHbmDuTHU2yBpqFq3ZzuqhL81nKrLMIfUarboDDg7h9Ru3lz+JEkagPsevg+Aex8u0zV0ZjgBh9Vq1ut2e2YNp+pgwKn69Qs4N20qQ223bm3+3CRJM86mxzcBsPHxjcCuNZyAEwdp1pso4DTDqUEy4FT92mephV1rOFvZTbOckqQB2Ly1/Peka8BphlMCulc8tW7RNm2Cww+HG25o/rw08xhwqn79ajgNOCVJA7T58SrgfKwEnJ3rcIIZTqlbhrN1i7ZuHaxeDTfe2Px5aeYx4FT9JlPDCQackqSBmHBIrRlOCZh4SO1PflJeH3qo2XPSzGTAqfq1erRnPau8tgec27aNfW/AKUkagJ1Dah+zhlPq5dFHxzKaMD7gfPDB8rpxY/PnpZnHgFP1awWU++9fXtsDzvaJggw4JUkD0Ao4H36iLDDYLcM5ms6KotntkUdg/vyxz+01nK0MpwGnBsGAU/XbsgX22mssw9lew9nOgFOSNACtIbUtXdfhdEitZrEnnoDt2+G5zx3b1l7D2RpK65BaDYIBp+oxOgp/+7dluZNHH4VnPrP8wfgMZ7tN428QJEl6MlqTBrV0reF0SK1msdbgs5/5mbFt7UNqW4GmGU4Nwtxhn4BmqOuvh6VL4TnPmXzAaYZTkjQAnRnOrjWcZjg1C330o2W47HveUz73Cjh3VP96GHBqEMxwqh733Tf22hlwOqRWklSjVg1ny7hlUcxwaha7/HL4whe6Zzgjdr01c0itBsGAU/X48Y/HXqea4fzJTyCzmfOUJM04Ew6pNcOpWez++8tfvyG1LWY4NQgGnKpHZ8D5jGeUP+gecD73uSXgfOghOOggWL682fOVJM0Imcmmxzex39P227nNGk6paN2WPfBA+dwv4HzssTIdh7Q7DDhVj/aAc8uW/hnOgw4qAecdd5Te7Xvfa/Z8JUkzwpZtW9iRO3jhvi/cuc0Mp1SWQWllNu+4o7x2BpydQ2qhZDm//GV4//vrP0fNTAacqsdEQ2o7azif/vSyENTmzbB+fdnWepUkaQpa9ZsH73vwzm3jlkUxw6lZ6v77x96vXVteO2s4219ba3Ru3Aif+Qx87GNWPOnJMeBUPaZSw7nvvuVv0yb40Y/KNgNOSdIUbB/dzrYd23bOUGuGUxqvPeBsZTj3338swOy8PfsP/6G8btwId99dhtY++GAz56qZxYBTg7N6NXz3u+X9VALO/fYrAWd7hrMVeEqSNAn/9fL/yq9d9ms7Jwx64X49Ak4znJql2gPOdevK6957955i40UvKq8PPQQ//GF533qVpsKAU4PzP/8nvPOd5f2Pf1x6rMceKz3VZDKcDqmVJD1J377n21y3/rquQ2rNcGq2Wru2LIn+ve91Dzgnuj1rBZw/+tFYZvPuu+s/Z808BpwanNWr4fvfL1XpjzwCP/uzZfvo6PhZajuLBFoB5xNPjBUVbN4MDz8Mf/3XcMwxzV6HJGla2bZjG3dtuosHtzzIXZvuAsYPqW1fh7MVfJrh1Gzwb/9WhsR+85slFzAyUmozH3usfP+MZ/SeYqM1pPaWW8baawWcP/oR7PBfIU2SAacG46GHYMOGMsB/5cqy7ed+buz7yWQ4oQSte+xR3v/oR2WF4quuciEoSVJPd266c2cAufLe8t+gA/c5cGeg2XVIrRlOzQLf//7Y6/33l2DzBS8o257+9BKA9ro9O+SQ8nrzzWPt/fCH5XbvRS+CT3+67rPXTGHAqSfviSfgvPPK65o1Y9v/9V/L61QCzv2q9dIefhhe9aryfv16uPXW8t5lUiRJPdz+k9t3vm8FnPs9bT/2fVp5mNl1SK0ZTs1QGzeOPae/7bax1/vvh+c9r/zB2G1Zr9uz/fcvt2etDOfee5cM53e+A1u3wre+Vf+1aGYw4NSTd/nlcOqp8KUv7X7A2cpwArzmNeX11lvHJg+69dYyduOUU+CmmwZ/LZKkaeWxbY9xzrXnsGXbFm5/aCzg/N4D32PunLk8Y49nsO9eXQJOM5ya4d76VjjhhPK+FXC2MpxTCTif8xx49rPL3I9z5pTbs7vvHrsNa71u2QL33FPvNWl6M+DU1NxzD9x7b3l/7bXl9VvfKj3ZHnvAPvuUggGAww8fKwSYaB3OXgHnlVeObbv1Vvj3f4fzz4dPfnLw1yVJmla+cNsXOOOfz2D56uXc/pPb2XevfTl434PZkTvYd699iQj2e1oZPTNuHc4qw/nY9sf41t2maDQzPP54ed2ypdRrfvOb8NOfluVPnv70cvt2xx3dA8699y6vnbdnz352+YMyDPdFLypDaluB5qpVZZDbmWfCK15R3kvdGHBqat7yFvi1XyvvW2MpvvWtkuE87DB4yUvGKtFf8AKYN6+8b580qF+G80UvKuM4/uVfxj7feit84xvlc+v1S1+Ct7+9TEokSZrxRnOU0Sx9/tfXfX3n6+0P3c6CeQtY8JwFADuH0nYdUltlOP/qur/idZ96Hd+9/7uNnb9Uh2uvLbdRN90E110H27fDtm3w2c+W9625FzdunHyGc6+9SqD6nOeUbS98IRx8cKnf/Pa3y3fbtpWpN1asKG23bgsvvtjFBjSeAad2NToKmeX9ypWwYEGZPXb16hL4XX99qam8+ebSS918c8k+/uzPloATyqD/vfaC5z63fJ7KkNoDDyx/W7eWR2tHH11+75//uXx/xx3lEduHPwyf/3zJqGbCn/5pOQ9J0ox07GeP5a2XvZXM3DXgfM5YwNnKbHYdUltlOK+56xoAlq9e3tTpSwPzp38Kn/hEef+pT5Xs4mc+UzKbEeXvb/6mfP+rvzp23HOfO/7WrP21/fasFWi2MpwHH1yCTijB5FvfWt5feincdVd5f9VVJeh95zvhj/+4bHvgAfj61wd11ZquhhpwRsQxEbEmItZGxBldvt8rIi6tvr8+Ig5p++7MavuaiDi6X5sRcWjVxu1Vm3v2+41Z49FHSz3m6Gipk3zDG8bW0/zzPy/B5sc+Bl/4wtgxf/iHZd93v7scd/fdJeBsLYXS6s0mE3Dut99YwDlnTnn0dsAB5fPLX17+Nm8umc0jjyzbP/lJuPHG8v7v/x6+9jX40IdKTWkmfOUrpYfdsqXsc8cdY++lJ+mp0GdJs8m6jev4b5f/N+5/5H5uuu8mvnbH1/jy97/M5Wsu50cP/4gjDjiC+x65j7s23VUCznlVhrMKNFuBZ7cMZ5IEwfLbZnbA2WS/pcG6/faSUYSSxXzNa8rtzNq1JeA8/XS47z744hfLPpddBtdcA698ZRni+t0qef+Wt5TZaGHyGc5WoNl6bWU4W972tjJw7fzzy+fDDiuVUBdeWD5//vNlSO/SpfCmN5V8xegonHUW3HBD2SezzBWpmW9oAWdEjADnAccCC4ETI2Jhx24nAxsz8zDgXOCc6tiFwBLgcOAY4PyIGOnT5jnAuZm5ANhYtd3zN6aN7dvH3m/bVjJ/LVdfDXfeWd5/97vw+79fArdNm+C1r4X//t/Lv4TvNtcAABjjSURBVO1Ll8Lxx8Nf/iVcdFF5PPaZz5T3X/5yGdz/6U+Xba97XZlF9qtfLY/Pfu/3xnqoyQac3Wo499mnfH7+82Hu3JLhhLGAE0qA+573wM/8TDnXOXPgqKNKD3vWWeXzt79dxnacfHI59z//85KlfelLy5iS7dvhH/4BfumXSpCcWYLX1kRHjz5aeutWhnfz5pJpbWlt16zzFOqzpGnvkSceYduObQA8uOVBPnXTp9i6fStbtm3hTZe8iZO+fBI7RnfwrhXv4lM3f4rfvfJ3+fgNH+cZezyDPUf2ZOn/WwrAR476yM42uw6prQLP9nU4WxlOgN99ze/y/Qe/z+oNq+u94CEZQr+lLjZuHLtde/jhcsuROXYLcs015bsvfhGOOKJMi/GDH5Tbrde9rhy/dGkJ1N773pIDmDu3PEd/+9vLbd1v/VaZYuOaa8otzutfX9o86KCSrTzssPJ5ooCz/fasM+Bsz3ACvPrVJaj96U/LQLh3vavcal58cblt27IF3ve+ks+AkhO44AL44AfLhEYPP1xyBM97XskfPPZYucZLLin7/+hHJXPb+ue2bt34FfJa1VuaHuYO8bePANZm5jqAiFgGLAbae/3FwIeq98uBT0Sp/F8MLMvMrcCdEbG2ao9ubUbEbcCRwG9U+1xctfvJXr+ROYDI4rLLSpX2CSeUXuCrXy2PnX7hF0q28Mc/hiVLyuOrSy8t/+YefXT5t/XOO8u/vZs2ld7o5S+Hd7wD/s//KUNY/+APyr9t73tfafOMM+D97y9zVf/BH5Te4qMfLdnDD32o/G3aVHq5ffYpg/yvu66Mg/j610u95fvfD896VglG7723/P7ISHlMdeyx5ZHaqaeWoOymm8ostAceWF5vvrkMp91nn3LtrUCzvVcbGSnDbLsNqZ0zp/x2K9BsDzhf9rKx/d/whpLlXLYM3vzmEvAee2wZVvvhD8O555bHbjt2wC//cvln8JnPlMdw3/xmqT+94ory/ZvfXP63uPjiMuHRX/wF/N3fleG7b397+f6000o96cc/XgLZz32uBO6/9Evl957xDPijPyr/LL/ylfK/9WtfW9qJKL3n979fxpm88Y3w8z9f/nk+8QSceGL5/8c//3M5j1e/uvx/5NFH4b/8F/jJT0od68teBv/xP5b3mzaVR4WP/v/tnXt0VeWVwH+bPAhJCCSE8Ajvgoo8ikCRCmJRZ0JxrBTaqbbLau3UqrXLV0t1MR3qo4updlal1jUWq6O02pbSsaVKB8EWFUtA5dEKFUiE8pA3yCPvkG/+2N8lJ/HeQJJ777mY/VvrrnvOdx7f3t9jn73P+b5zKlSf887T+i8thUOHVOe6Oi2PAQN02/r1egt00iSVafVqrZcxY1TXPXv0CpeRocOlCwt125Yt2j7Gj9fJGmvWaF2NHattobxcr4bdumn+2dm67/bteuyYMTqHt7RUr4wTJqi+mzdrvfburbI4B5dcom1uwwbVd+BA1a+2Vst63z690o4cqTqvXKllcMUV2n9ee01fUjVqlLbnw4dh+vSmV8f2kyo2Ky7UN9Szcd9G9pzYw/i+48lKz2LDvg3kZ+UzomgEu47t4v0T7zO853C6pHdhy+EtZGdkM7RgKAcrDrLv5D4G5w8mOyOb7Ue3k5mWyYBuAzhWc4z9J/dTnFdMdkY2e47vIa1TGn1y+1BZV8mBigP0yu1FdkY2+0/ux+HondubmvoaDlYepEeXHmRnZHO46jCnGk7RM6cndafqOFR5iO5Z3cnOyOaD6g+oa6ijMLuQUw2nOFx1mLzOeXRJ78KJ2hPU1NfQI7sHDa6Bw5WHyc3MJTsjm4q6Cqrrq8nPUg/qSNURsjOyycnMoaK2gsq6Sgq6FJze1iWjC7mZuVTWVVJRW0F+l3wE4Wj1UTqndSY3M5eq+ipO1JygoEsBaZ3SOFx5mMy0TPI651FVX8XxmuMUdCkgvVM6hyoPkd4pnfysfKrqqzhadZTC7EIy0jI4WHEQEaEwu5CquioOVR6iZ05PstKzTpdTr5xeVNVXse/kPopyisjJyGHvyb3UN9TTL68fVXVV7Dq+i6KcIvKz8tl5bCfV9dUMyR9CVX0V5UfK6ZXbi965vSk7UsaJmhMM7zmc6vpqNh3YRJ+ufRjYbSCbDm7iUOUhxvUZR82pGkp3l9K3a19GFo1k7Z617Dq2iykDp1DfUM/SbUspzivmsoGXsax8Ge8ceIcZF8xAEBa8vYDivGKuG3kdT61/ipU7VnLzuJvJSs/ijv+7g6KcIh6c+iBz/jSHsiNlPLvxWfI6550eKrv18FZKd5dycfHFLNq0iDRJ42tjv0ZlfSULNy5kSP4Qpg6eytCCoZQdKWNYwbDTgWbkyWZLTzhH9xrN7Emzmb9mPos3L+a7U77Lur3reLn8ZUYWjeSCwgv44V9+yM7jO7lr4l0crznOgrcXMK7POG4ccyO/2fwbyo+Wc9OYm8hKz2LRpkUMLRjKjAtmsGrnKrYd2cZVw66ia+euLC9fTu/c3kwZOIVNBzdRuruUuybe1eRlRgkiaXar2TnbzJIl6kp84hN6D33zZnUzevXSS5uIXjJ27dJLxujRGlS9+mrjIK3du/WSNXq0BkMrVmgAVFLSGJR9/OP6e+kl/ZT4jBnqlr34oh43eTIsXqyXyC9+US8rzz2nl5mrr9Z78lu36kCv48fh0Uf1MvTVr6o78eab6prV1uqTyGHDNNi67z497oYb9LL7s5/pJfLb39Z76bW1Kmf37ppeVqaX3R079LL24ovqTt14Y6NrmZ+v7uHixeoaTpmiTxMfe6xxptPw4Xpp7t27dUNqI/8DBqirGNnWt6+6AKtX6/38khLV9+RJdcXuuEMDzPx8lfVHP9InoKNGqetx2WXqnnTurK7ZhRfqYLUnn1T34sknVb/Fi2HqVHW1Cgv1a3zPP6+v8Zg9WwPrBx7Q8po7V+t26VJ1mSdMUBc6MxNuu00/77J8ubqN48apK9nQoPW7fbs+p5k0SfV66SV9EdNnPqPt4vXX1a0ZPVrzOHlS3bFjx7Rdnn++bist1cB4yhQ9vrQUBg9W92XdOnVZLrlE8127Vgf0jRypZbJvn7b7Tp20/RQVaXm9+662w7Fjtbzeekv1HT1a28c//qGy5eTottxcbds7dmhZjh6t+7/5ph4/dqw+c9m6VfPu2VNlSUvT/CPtIZ6EGXAWA8GXKO8GLo61j3OuXkSOAT18emmzY/0YzKjn7AF84Jyrj7J/rDwOtVmzCMuWqUX61reib+/UCb7/fV3u3Lnpk7S8vMbbPH37ai985BHtNUOGaE8C7U3r1mlPz8/XgOeRR3TbV76iLe/OO/WYhx/WgLG2Vm8bvfGGWrpJk/S22kUXae+eP19vJV17rQZe06apY//KK2oVqqo0OJ00SfOZPFmt/vnnayuNDIuFxv/IK9C6dlULCmppofEbnPn5jYFm//76P2qUBjQDBmjP6969MeD80pc0iOvVS2+BffObeiW6915dnjNHZdq7VwOSp59WfceNU+s0c6Za39mz1Vrceada0dtv1zEiixapVdi7t3E8yic/qRYtolt1tT5JBX06+/LLupzpRz8++mjjemQyRYQ5c6K3C9DPvxjt5/rr9YZDfEgVm9VuVu1cxbRfTKOirqLVxwqCw0Vd7ySdTr/Qpfl6821pknb6O4jB5TNtS++UTn1D/Vlta3ANp2XL6JRBXUPdaVmcc1G3CYKInJb1bLc1lycoS2u2tVQWrSnf4HpLdRZvBOEHb+hAodzMXCpqK3jwtQcRhPN6nMfXX/w6ABP7TeT9E+/zhcVfoDC7kAc+9QAPvf4Qtadq+fG0H1N+tJz5a+Yzqf8kVnx5BeMWjGPzwc3cPuF2quurWbhxIVcMvgKAKwdfqQFnj2HkZuaSJml076zXlfwuenMhEmQCZKapfZ41fBZ9uvZh8oDJ3P/q/cxbNY/q+uom+mSmZdKjSw9KfqGjSYu7FrPivRX85xv6ZLVrZlee2fCM5uHr6paXbjl9/H2v3BeznD534ecY0G1A1O1xJJl2Ky7cc4860cnmnnuip6enN7pVOTnqPt19t7obPXo0zjYaPFiD3J/+FLKyNPi8xTeFyy/XN7rOmqWuzK23Nr5wf/ZsDdrmzdNj5s/X4HfnTvjDH9TFmztXXbEXXtDgYcsWlXf/fg04Z85UF+rqq9V1mTy5cUDW8OGN/7/7nbou3bqp29m1q26LPCuIuGfp6Y2BZuTdjwMHqttWXKxBrEjjZ9NLSjTA6d1bdZ86VQPvu+/WQPrWW7XcampUhsceU/eopETd4EsvVfcpcm///vvVHZw7Fx56SAPIq67SIcYzZ6rsV16pZTZvnpb91q3qogEMGtRY9tnZeiPi8cd1PStL3cEgkfmm0eho7lhamtbJd74T3/NKPB7ktSljkc8DJc65f/Pr1wMTnHPfDOyzye+z26+Xo3fXHgBWO+d+4dOfApaiQ4Q/dM7A/kN9en9gqXNuVKw8nHOHm8l7M3CzXz0f2EJyKSQeQXBqYTqdG3QUnQY653rGOiBVbFYUudpqm8Ku1zDz78i6h52/6d42WrRPsUim3QqeM3DuMH2nsNtaS5hsbSeV5euIsp2VbQrzCeduoH9gvR/wfox9dotIOtANOHKGY6OlHwK6i0i6f2IQ3D9WHk1wzi0AFrRSx7ghIm8558aHlX8iMJ3ODUyn06SKzWpCW21T2PUaZv4dWfew8zfdk553Mu3WhwjTdwq7rbWEydZ2Ulk+ky02Yb6l9k1gmH8TYyY6MX1Js32WADf45c8Bf/JzK5cA1/o3qw0GhgFrY53TH/Nnfw78OX9/hjwMwzCCpIrNMgzDOFuSZreSoIthGOcooT3h9PMEbgeWAWnA0865TSLyAPCWc24J8BTwcz9R/Qhq1PD7LUInqNcD33BOJ7lEO6fP8jvAr0TkIWC9Pzex8jAMwwiSQjbLMAzjrAjBbhmGYXyI0OZwGq1DRG72Q1M+MphO5wam00eTsMsgzPw7su5h52+6d2y7k0xSubxNtraTyvKZbC3kbwGnYRiGYRiGYRiGkQjCnMNpGIZhGIZhGIZhfISxgDOJiMj3RGSPiGzwv+mBbfeJSJmIbBGRkkD6NJ9WJiL3BtIHi8gaEdkmIr/2E/fxk/t/7fdfIyKDzpRHsomlU9iIyA4R+Zuvm7d8WoGILPflvFxE8n26iMiPvQ5/FZGxgfPc4PffJiI3BNLH+fOX+WOlpTzaqMPTInJARN4JpIWmQ0t5tFMn60sqx+dFZJOINIjI+ED6IBGpCpTPE4FtcatDEfmJiNSIiBORuYH0fxKRt30+b4vI5YFtK325RWQr8umtKm+v+z983rua1Wmy28CrAX12iMiGJNdDaP1BRB4RkXe9TC+ISPdk6n62xNK3DefpLyJ/FpG/i/a9O3x6wuugoyMx7J3flvA+30pZz8n2EK9+0oZ8E+p/tVKWUPyodsqX+u3NOWe/JP2A7wHfipJ+IbAR6AwMBsrRifhpfnkIkOn3udAfswi41i8/Adzql28DnvDL1wK/bimPEMogpk5h/4AdQGGztIeBe/3yvcAP/PJ04I+AABOBNT69AHjP/+f75Xy/bS3wSX/MH4FPt5RHG3WYAowF3kkFHWLlEQedOnxf8rIMR79ttxIYH0gfFCyvZsfEpQ59+9iFfq9vFfoJhUg7uQjo65dHAnsC+TeRNZDeqvIGRgA70Q/TT4zUadhtAPgv4D+SVQ8p0B/+GUj3yz8IyJsU3c+yn8TtugP0Acb65a7AVl/OCa+Djv4jtr1LeDtvg6znXHuIZz9pQ947SKD/1UpZQvGj2ilfyrc3e8KZGlwD/Mo5V+Oc2w6UoU7cBKDMOfeec64W+BVwjb8bcjmw2B//LDAjcK5n/fJi4Aq/f6w8kk1UnUKQ42wJlmfzcl7olFL0m4l9gBJguXPuiHPuKLAcmOa35TnnVjvtxQuJXmfBPFqNc+41Pvwd2TB1iJVHe3WKRUfqSzjn/u6cO+sPqce5DkuApc65tegbLNcA07xc651zke/ybQKyRKTzGcRrbXnnAX8Hqn3+EVsSWhvw2/4V+GVLiiaxLyW8LJxzLzv9Vixo8N8vRXQPErfrjnNur3NunV8+gbbB4hYOiWcddGhasHfJ6PPxIpXbQ6r5Z3HxXVqbaYh+VHvki0XKtDcLOJPP7f6x+9PSOHSyGH1SEGG3T4uV3gP4IHCRj6Q3OZfffszvH+tcySZV5IiGA14WHQJ4s0/r5ZzbC+poAEU+vbV1VuyXm6e3lEe8CFOHRNZ3R+9LZ2KwiKwXHe55qU+LZx02Tz9A9HKYBax3ztUE0v7HD/v5bsCZa215xys9nm3gUmC/c25bYFui6yFCWP0hyE3oHftk634mEtJnRYdbXoTebIHE14ERnWS387PlXGsPYV7bEul/xYNk+FHtJaXbmwWccUZEVojIO1F+1wD/DXwMGAPsRYdegT5Wb45rQ3pbzpVsUkWOaExyzo0FPg18Q0SmtLBvPOssLJKhQ6L07jB96Qw2JRZ7gQHOuYuAu4HnRSSPtsk+EVgYyRe4GL0bOuJM5xKREegwy68Hkr/knBuFBmeXAtdHdo9yvt8C1wHzAvl/Fhjfgi4JaQMisgJ9evd6M5muCRxzHU2fbia8HpJxbfG6DwVWBPLvR+DpgYjMQZ80P+eT4ql7e/tc3PusiOSi7fNO59xxkmOTPvK00d4lw+63VtZzsT2E2fYS6X8lklSpz5Rvb+nxOInRiHPuyrPZT0SeBF70q7uB/oHN/YDIcLRo6YfQx/bp/i5EcP/IuXaLSDrQDX303lIeySRV5PgQkSGAzrkDIvICOuRgv4j0cc7t9UMhDvjdY+mxG/hUs/SVPr1flP1pIY94EaYOCalv59z+yPJHvS+drU1pdkwNUOOX3xaRcuA82laHvwVWOud+CSAiW9D2EflFKAJei6yISD/gBeDLzrnygGx7/P8JEXke7WcLiV7eQ9H5Mjjn5vnzLgN+70/XmrqOlX5WbQANrvahc2Kay3QbsB+YCYwL6JrweojcdY+QiP7gnCvx5f4959xqXz/78MGl6Asx/gW4wg8Ti7fu7e1zce2zIpKB1sdzzrn/haTZpI88bbF3JMfut1nWc6g9hOafJdj/igfJ8KPazDlhf1wSJgPb7/Tk3T6B5bvQcdWgTwqCk3rfQyf0pvvlwTRO6h3hj/kNTSf13uaXv0HTCe+LWsojhDKIqVPIdZMDdA0s/wV1MB+h6UTxh/3yVTSdKL7WpxcA29FJ4vl+ucBve9PvG5koPt2nR82jHboMoulk8tB0iJVHHHTq8H2pWfmspOlLNHrS+BKbIcCeeNdhs3ayqlke3X0ZzWomZzr+xRBABjpP5Ja2lHegToMvDRoRYhuYDrzaTN+E10MK9IdpwGagZxi6n2X/iNt1x8uwEHi0WXrC68B+Me1dwtt5G2Q859pDPPtJK/NNuP/VBpkGkWQ/qp3ypXx7C8VYdNQf8HPgb8BfgSXNGsgc9I1RWwi8sQp1Yrb6bXMC6UPQN12V+cbR2adn+fUyv33ImfIIoRyi6hRy3QzxHW4j+pKTOT69B/AKsM3/RwyGAI97Hf5G04vfTb78y4CvBNLHA+/4Y34CSEt5tFGPX6LDKerQO1tfDVOHlvJop07Wl1SOz/oyqUGfsC3z6bN8O94IrAOuTkQdAo+hwygdOtcpkv+/AxXAhsCvCHUm3vb1tgmYT2NQ0qry9rofAhq8DNvCbAPAM/jgObBPsuohtP7g13cF6vmJZOreir4Sl+sOMBlt738N6Dw9GXXQ0X/EsHfJ6vOtlPWcbA/x6ietzDPh/lcr5QnFj2qnfCnf3iJG3jAMwzAMwzAMwzDiir00yDAMwzAMwzAMw0gIFnAahmEYhmEYhmEYCcECTsMwDMMwDMMwDCMhWMBpGIZhGIZhGIZhJAQLOA3DMAzDMAzDMIyEYAGnYRiGYRiGYRiGkRAs4DQMwzAMwzAMwzASggWchtEMERklIm8E1seKyJ/ClMkwDMNsk2EYqYrZJ6MlxDkXtgyGkVKISCfgfaDYOXdKRP4M3OOcWxeyaIZhdGDMNhmGkaqYfTJaIj1sAQwj1XDONYjIJmCEiAwDdprBNAwjbMw2GYaRqph9MlrCAk7DiE4pMAm4DZgWsiyGYRgRzDYZhpGqmH0yomIBp2FEpxR4BnjcObcnZFkMwzAimG0yDCNVMftkRMXmcBpGFPxwkFeBYc65irDlMQzDALNNhmGkLmafjFjYW2oNIzp3APeZwTQMI8Uw22QYRqpi9smIigWchhFARD4mIu8CXZxzz4Ytj2EYBphtMgwjdTH7ZJwJG1JrGIZhGIZhGIZhJAR7wmkYhmEYhmEYhmEkBAs4DcMwDMMwDMMwjIRgAadhGIZhGIZhGIaRECzgNAzDMAzDMAzDMBKCBZyGYRiGYRiGYRhGQrCA0zAMwzAMwzAMw0gIFnAahmEYhmEYhmEYCcECTsMwDMMwDMMwDCMh/D/y2swvMVS4XAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_Y^{do(X)}(y)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'interventional', 't dist', lambda x: x, val_x = xbins[idx[i]], df = 1)\n",
    "    sns.distplot(y, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$y$\")\n",
    "    ax[i].set_title(\"$do(X = %.1f)$\" % xbins[idx[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "smAj0d_OuGTj",
    "outputId": "7824d5db-bb8d-4132-baef-7c53f6cd0d35"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Mohammad Reza\\Anaconda3\\lib\\site-packages\\scipy\\stats\\stats.py:1713: FutureWarning: Using a non-tuple sequence for multidimensional indexing is deprecated; use `arr[tuple(seq)]` instead of `arr[seq]`. In the future this will be interpreted as an array index, `arr[np.array(seq)]`, which will result either in an error or a different result.\n",
      "  return np.add.reduce(sorted[indexer] * weights, axis=axis) / sumval\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_X^{do(Y)}(x)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'normal', 'interventional', lambda x: 0, val_y = ybins[idx[i]])\n",
    "    sns.distplot(x, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$x$\")\n",
    "    ax[i].set_title(\"$do(Y = %.1f)$\" % ybins[idx[i]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Og1NhEzdg1bK"
   },
   "source": [
    "Intervention on $Y$ does not change the distribution of $X$, and $P_Y^{do(X=x)}(y) = P_{Y|X}(y|x)$. Consequently, we conclude $X \\rightarrow Y$, which supports our previous inference. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "fqU8HXUH3umt"
   },
   "source": [
    "##### Causal Discovery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "BbNu7VDp3wmJ",
    "outputId": "c0065804-3def-49db-cd0d-c02a52338b92"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 1\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.018705123186506162 \n",
      "\n",
      "Step 2\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.050059845795471646 \n",
      "\n",
      "Step 3\n",
      "-> HSIC(x, r_y) p-value = 0.5658278067254578\n",
      "-> HSIC(y, r_x) p-value = 0.09276981343038904 \n",
      "\n",
      "Step 4\n",
      "-> HSIC(x, r_y) p-value = 0.17304080591364474\n",
      "-> HSIC(y, r_x) p-value = 0.0043103561556376855 \n",
      "\n",
      "Step 5\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.008366763927969239 \n",
      "\n",
      "Step 6\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.04786758123022795 \n",
      "\n",
      "Step 7\n",
      "-> HSIC(x, r_y) p-value = 0.48424701355645794\n",
      "-> HSIC(y, r_x) p-value = 0.10021791452933307 \n",
      "\n",
      "Step 8\n",
      "-> HSIC(x, r_y) p-value = 0.5201528671012019\n",
      "-> HSIC(y, r_x) p-value = 0.007074075128981522 \n",
      "\n",
      "Step 9\n",
      "-> HSIC(x, r_y) p-value = 0.19911722078657057\n",
      "-> HSIC(y, r_x) p-value = 0.03922314583048 \n",
      "\n",
      "Step 10\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.022077218816012108 \n",
      "\n",
      "HSIC(x, r_y) p-value average =  0.6942385714083332\n",
      "HSIC(y, r_x) p-value average =  0.039067183803100834\n"
     ]
    }
   ],
   "source": [
    "p_x = []\n",
    "p_y = []\n",
    "\n",
    "for i in range(10):\n",
    "    print('Step', i+1)\n",
    "\n",
    "    x, y = get_data(200, 'normal', 't dist', lambda x: x, df = 1)\n",
    "    r_y = fit(np.expand_dims(x, axis=1), y)\n",
    "    r_x = fit(np.expand_dims(y, axis=1), x)\n",
    "    p_x.append(Hsic().test(x, r_y, workers = -1)[1])\n",
    "    p_y.append(Hsic().test(y, r_x, workers = -1)[1])\n",
    "\n",
    "    print('-> HSIC(x, r_y) p-value =', p_x[-1])\n",
    "    print('-> HSIC(y, r_x) p-value =', p_y[-1], '\\n')\n",
    "\n",
    "print('HSIC(x, r_y) p-value average = ', sum(p_x) / len(p_x))\n",
    "print('HSIC(y, r_x) p-value average = ', sum(p_y) / len(p_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Gm_FNvKHVkn5"
   },
   "source": [
    "Anti-Causal: $Y \\rightarrow X$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9E1B6Dt7uGTl"
   },
   "source": [
    "$N_X\\sim \\mathcal{N}(0, 1),\\ N_Y \\sim$ Student's t-Distribution with degree of freedom $= 20$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "66CfIU5TuGTm"
   },
   "source": [
    "##### Observational Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 436
    },
    "id": "4lyje0R2uGTm",
    "outputId": "1336e808-9c1e-4c2f-df8e-69255472ea5b"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "Xgrid = np.linspace(-4, 4, Ngrid + 1)\n",
    "Ygrid = np.linspace(-100, 100, Ngrid + 1)\n",
    "xbins, ybins = plot_observational(100000, 'normal', 't dist', lambda x: x, Ngrid, df = 20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "x_4cJX51uGTq"
   },
   "source": [
    "##### Interventional Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 461
    },
    "id": "gYD9MF0auGTq",
    "outputId": "11feaca1-ba27-41c4-ddd2-291c63b9e876"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_Y^{do(X)}(y)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'interventional', 't dist', lambda x: x, val_x = xbins[idx[i]], df = 20)\n",
    "    sns.distplot(y, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$y$\")\n",
    "    ax[i].set_title(\"$do(X = %.1f)$\" % xbins[idx[i]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 459
    },
    "id": "2Vdij8iquGTu",
    "outputId": "5facd75f-6046-4da3-d9be-3e6a02467f88"
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.6/dist-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `kdeplot` (an axes-level function for kernel density plots).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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pjU1EpA+n2k7x460/5n0V72OYDfw/tbcv9Pupf7z1x+kOTUTyzPe/788tHNv/Fe2Av/7uu+HJJ6GtLTOxSbwoMZR4a2qCrVsvnrY6GO96l3/VPkMRyZKfbfsZbZ1t/Erp4NquhUULmTZmGi/vejnNkYlIPtmyxf/0t+hMT+9/Pxw5ouqk+UKJocRblMxFyd1gzJrlj61YsyY9MYmIXMFzTc8xtnAsb53z1kHdb2bcMPsGJYYiMiRRiYVf/dXB3f/ud/vqpFpOmh+UGEq8Pf88zJzZ/0Pt+3LLLfDzn/tDeUREMsg5x3PNz/GO+e+gsKBw0M+5YfYNtBxt4cCpA2mMTkTyyfe/D1VVMHfu4O4fMQJ+/dfhv/7L1wGU3KbEUOLLOZ8Y3nyzP5NwKG65BY4fh3Xr0hGZiEifth/bzo7jO3jXgiGsdIALRWt+ufuX6QhLRPLM0aPwi18Mfhlp5P774cwZf+SF5DYlhhJfjY1w4IBP6oYqqmiq5aQikmEv7fK13Qe7jDSy/OrljBg2gl/uUmIoIgP3gx/4hVKDXUYaueEGmD8f/vmf0xOXxJcSQ4mvKIkbzDEVPV19NZSVKTEUkYx7ceeLjB85niVTlwzpOaOGj6J6ejVr965NU2Qikk+efhqKi2HVqqE9Z9gw+NCH4Kc/hV270hObxJMSQ4mv55+H2bNhwYL0PC/aZ9jenp7niYj04qVdL3H9rOspGFYw5GetnLGSmr01dLmuNEQmIvmiowOee86f2FUw9KaID37Q7/D5l38Z+rMkvpQYSjylc39hZPVqOH0aamrS8zwRkR6Onj3KpoObhryMNLJq5ipOtp1k86HNaXmeiOSHl1/2ewyHur8wUlIC110H//qv6XmexJMSQ4mn+npobU3P/sLITTf51xdeSN8zRUS6iQrF3Dj7xrQ8b+XMlQC8tue1tDxPRPLD00/7iqLvfnf6nvkbvwHr1/tzESU3KTGUeHr+ef+ajv2FkeJif+zFq6+m75kiIt28tPMlCqyAVTOHuKknZfHkxYwrHKfEUEQG5Omn/Xj4uHHpe+Z73+tfn3wyfc+UeFFiKPH04ov+YPp589L73Guv9Ymhc+l9rogI8OKuF1l+9XLGFI5Jy/MKhhWwYsYKFaARkX5raYGGhvQtI43MmuWXk37/++l9rsSHEkOJH+f8wTtvfWv69hdGrr0W9u2D3bvT+1zJKWZ2m5ltNrNmM3uwl88/bma1ZrbezF40s4rU+/PM7Gzq/fVm9n+zH72E0tbZxmt7XkvbMtLIyhkrWb9/Pec7zqf1uSKSm555xr+mOzEEuP12WLsWDh1K/7MlPCWGEj87dsCePT4xTLdrr/WvWk4qfTCzAuBh4HagArgvSvy6edw5V+Wcqwa+DHy122ctzrnq1M/HsxO1xMG6fes413GOG+ekNzFcNXMV7V3tbDiwIa3PFZHc9Mwz/oSukpL0P/u22/z4/Y9+lP5nS3hBE0ONykuvXnzRv2YiMVy2DAoLlRjK5awCmp1zW51zbcATwN3dL3DOnej26xhAa5OFV/f4duX6Wden9bnRfsW1e7ScVNR3kss7edKXacjEbCHAihUwZYo/CkNyT7DEUKPy0qcXX4Tx42HJ0A6H7tXIkVBVBevWpf/ZkitmAt2P8N2deu8SZva7ZtaCb5s+3e2j+Wa2zsxeMLO3ZTZUiZO1e9cyY9wMZo5/0z8uQzJr/CymjZl2IfGU/KW+k1zJT34CbW3+/MJMGDYM3vEOWLNG5RpyUcgZQ43KS+9efBFuvDE9J7L25pprfGKoFk2GwDn3sHOuBPgj4HOpt/cBc5xz1wCfAR43s/G93W9mD5hZjZnVtLa2ZidoyajX9rzGyhkr0/5cM+P62dfz4s4X0/5sSRz1neSyfvITGDvWd6My5a1v9Tt+du7M3HdIGCETQ43Ky5sdOQJ1dZlZRhqprvbfs2vXla+VfLQHmN3t91mp9/ryBHAPgHPuvHPucOrPrwMtwKLebnLOPeacW+GcW1FcXJyWwCWcY+eOseXwlrQdU9HT6nmr2XZsG9uObsvI8yUx1HeSy/r5z31SOGJE5r4j6qK99FLmvkPCiH3xmaGMymtEPoGiViaTieE11/hXLSeV3q0FSs1svpkVAvcCT3W/wMxKu/16B9CUer84tdQLM1sAlAJbsxK1BFWztwYgIzOGAKvnrwZgzfY1GXm+5Bb1nfLT4cOwaRO8/e2Z/Z6qKn8+4otaxJBzQiaGGR+V14h8Ar34oh/mWpmZzhUAS5f6YzDWr8/cd0hiOec6gE8BPwQagCedc3Vm9iUzuyt12afMrM7M1uM7WB9Ovf92YGPq/X8HPu6cO5Llv4IEEB1Av2LGiow8v6K4gqljpioxFPWdpE9RopbpxLCgAK6/XolhLhoe8LsvjMrjG7V7gfu7X2Bmpc65ptSvl4zKA0ecc50alc8xr7wCy5fDVVdl7jvGjoVFizRjKH1yzj0LPNvjvc93+/Pv93Hfd4HvZjY6iaO1e9dSWlTKpKsmZeT5ZsYt827hZ9t+hnMOS/cZr5IU6jtJn37xC19jL5Nj65HrroM//3M4cwZGj87890l2BJsx1Ki8vElXF7zxRnZatCVLoL4+898jInnhtT2vZWx/YWT1/NXsPbmXLYe3ZPR7JL7Ud5LLee01v1tm5MjMf9fy5b7btnFj5r9LsifkjKFG5eVSW7bAqVPwlrdk/rsqKuB734Nz52DUqMx/n4jkrD0n9rD35N6M7S+MRPsMf7btZyyesjij3yXxpb6T9Karyy+E+shHsvN9y5f71zfe8LOHkhtiX3xG8kiNL97Aiszs0blERYVvRbdo5F1EhmbtXn/wfKZnDEsmlTB7/Gx+tv1nGf0eEUmebI6tA8ya5Q+6f+ON7HyfZIcSQ4mPmhq/UL2sLPPfVZE6D1jLSUVkiGr21lBgBVRPr87o95gZq+evZs22NXS5rox+l4gkSzbH1sHX8Fu+XIlhrlFiKPHx+uv+jMHhWVjhvGgRDBumxFBEhmzDgQ2UTSnjqhEZLJqVsnr+ag6fPcymg5sy/l0ikhyvv+7r9mVjbD1yzTX+eIy2tux9p2SWEkOJh85OP+yUraGuUaOgpESJoYgM2Yb9G1g2fVlWvuuWebcAfp+hiEjkjTdg2bLsjK1HqqqgvR2amq58rSSDEkOJh8ZGX/M4W4kh+OWkSgxFZAiOnD3CrhO7WDYtO4nh7AmzWVi0UImhiFzgnJ+5W7o0u99bWelf6+qy+72SOUoMJR6ixfHZ2jUNPjFsatIaCBEZtNoDtQAsnZa9Htnqeat5YccLdHR1ZO07RSS+9u2DI0f8DF42LV7sd+UoMcwdSgwlHl5/HcaM8a1MtlRUQEcHNDdn7ztFJKdsOLABIGszhgA3zbuJE+dPXEhKRSS/bUptOV6yJLvfe9VVsGCBFl/lEiWGEg81NX4Xc0FB9r4zWgOhFk1EBmnjgY1MGT2F6WOnZ+07r5vlDw17bc9rWftOEYmvUIkh+K6UZgxzhxJDCa+zE9avz+4yUvCzk2ZKDEVk0Opb66ksrsTMsvad8yfOZ8roKby659WsfaeIxFdtLUyf7s8VzDbtysktSgwlvK1b4ezZ7O+aHj0a5s9XYigig+Kco+FQA+VTyrP6vWbGqpmrlBiKCOBnDEPMFoKfMezoUGXSXKHEUMLbuNG/ZjsxBFUmFZFBO3D6AMfOHaO8OLuJIcC1M6+lobWBE+dPZP27RSQ+nIOGBijPfjMEqDJprlFiKOHV1volnRUV2f/u8nLYvNkvZxURGYCG1gaArM8YAqyauQqH4/W9r2f9u0UkPvbsgdOnwyWGUWVSjbHnBiWGEt7GjVBa6pd2Zlt5uV8Yv3179r9bRBKt8VAjQJAZw6gKau1BVSYVyWeNvhmirCzM90eVSTVjmBuUGEp4tbXZP3wnErWkUcsqItJPDYcaGFs4lpnjZmb9u6ePnc7kqybryAqRPBc6MQTtysklSgwlrNOnoaUlXGIYnZuoxFBEBqjhUANlU8qyWpE0YmYsmbpEM4Yiea6xEcaP91VJQ6mshC1bVJk0FygxlLDq6vzO6RCFZwCKimDqVCWGIjJgDa3Zr0jaXdXUKupa6+hyXcFiEJGwGhv9bGGA8akLVJk0dygxlLBqU6PdoWYMwbeoSgxFZABOnD/BnpN7wiaG06o41XaKHcd2BItBRMKKEsOQotqB2meYfEoMJayNG33RmQULwsWgxFBEBmjzoc1AmMIzkaqpfkBNy0lF8tPJk74qaejEMJqxbGgIG4cMnRJDCau21p/KOizgP4qLF8OhQ/5HRKQfGg6FO6oiEiWlUZIqIvllc+pf/dCJYVSZVAVokk+JoYTjnJ8xDLW/MBK1qJvVuRKR/mlobWDEsBEsmBRutcPEUROZMnoKWw5vCRaDiIQTh4qkkYoKLSXNBUoMJZz9++Hw4bD7C0FHVojIgDUcamBh0UJGFIwIGseiyYtoOqKKDyL5qLERCgqgpCR0JD4x3LIF2ttDRyJDocRQwtm40b+GnjGcOxdGjlRiKCL91nCoIej+wkhpUakSQ5E81djok8LCwtCR+Mqk7e3+BDJJLiWGEk4cKpKCH25btEiJoVxgZreZ2WYzazazB3v5/ONmVmtm683sRTOr6PbZH6fu22xmt2Y3csmGts42Wo60BN1fGCktKmXvyb2cajsVOhQRybI4VCSNqDJpbgiaGKrzledqa2HGDJg8OXQkvmXVHkMBzKwAeBi4HagA7uve9qQ87pyrcs5VA18Gvpq6twK4F6gEbgMeST1PckjzkWY6XWcsEsNFkxcBPibJD+o7CVw8NzAuiWEUhwrQJFuwxFCdL2HjxvCzhZGyMti6Fc6fDx2JhLcKaHbObXXOtQFPAHd3v8A5d6Lbr2MAl/rz3cATzrnzzrltQHPqeZJDGlpTFUnjsJR0cikATYe1nDQfqO8kke3boa3NF1aPgzFjYN48JYZJF3LGUJ2vfNbR4VuPOCWGnZ1aHC8AM4Fd3X7fnXrvEmb2u2bWgu94fXog96buf8DMasysprW1NS2BS3ZER1Usnhy+R7awaCGA9hnmD/WdBIhXRdJIZaWWkiZdyMQwK50viaktW/xQV+jCMxFVJpUBcs497JwrAf4I+Nwg7n/MObfCObeiuLg4/QFKxjQcamDuhLmMKRwTOhTGFo5lxrgZOrIif6jvJMDF7kpcZgzB7zPcvNmP/Usyxb74zFA6XxqRj7GoImlcZgwX+X06SgwF2APM7vb7rNR7fXkCuGeQ90oCNR5qpGxKfIbpVZlUelLfKfc1NkJxcTzKNEQqKvyY/9atoSORwQqZGGa886UR+RjbsAGGD4fy8Ht0ABg7FmbPVmIoAGuBUjObb2aF+D05T3W/wMxKu/16BxD1yp8C7jWzkWY2HygFXstCzJIlXa6LxkONsSg8EyktKtUew/yhvpMA8apIGokqk2qfYXKFTAzV+cpnGzb4pHDkyNCRXFRWpsRQcM51AJ8Cfgg0AE865+rM7Etmdlfqsk+ZWZ2ZrQc+A3w4dW8d8CRQD/wA+F3nXGfW/xKSMTuO7eBM+xkqp1aGDuWCRZMX0XqmlWPnjoUORTJPfScB4pkYRmP92meYXMNDfbFzrsPMos5XAfCNqPMF1DjnnsJ3vt4JtANH6db5MrOo89WBOl/Js2EDrF4dOopLlZXBP/0TOAdmoaORgJxzzwLP9njv893+/PuXufcvgL/IXHQS0qaDmwCoLI5PYti9MunKmSsDRyOZpL6TABw6BIcPxy8xHDfOVyaNjqmW5AmWGII6X3nr0CHYuxeWLQsdyaXKyuDkSdi3z5+vKCLSQ12rHwqP04xhaVEqMTyixDAfqO8kcaxIGlm69GIZCUme2BefkRy0YYN/ra4OG0dPUQvb0BA2DhGJrU0HNzFnwhzGjxwfOpQLSopKMEz7DEXyRLRUs6LnCZYxsHSpLzx/7lzoSGQwlBhK9kWJYdxmDLVrWkSuYNPBTbFaRgowavgo5kyYo8qkInmivt4fKD9nTuhI3qyqyh8LrTH2ZFJiKNm3YQNcfbWvsxwn06b5us9aHC8ivejo6qDhUANLpi4JHcqblBSV0HK0JXQYIpIFdXW+0MuwGPbio+OptZw0mWXoP3IAACAASURBVGL4j5TkvA0b4jdbCL7gTFUVbNoUOhIRiaGWIy20dbbFMzGcVELLESWGIvmgvh4q47Vw4YKFC2HUKCWGSaXEULKrrc23aHFMDAGWLPGJoXOhIxGRmIljRdJIyaQSWs+0cuL8idChiEgGHT3qa+TFcX8h+COqKyuVGCaVEkPJrsZGaG+Pb2JYVeUrk+7YEToSEYmZTQc3YRjlxfE53D5SUlQCoFlDkRwXlUGI64whqDJpkikxlOyKa+GZSFWVf9VyUhHpoa61jgWTFjB6xOjQobzJwqKFANpnKJLj4lyRNLJ0KRw8CAcOhI5EBkqJoWTXhg0wciQsWhQ6kt5FQ3AqQCMiPWw6uCmW+wvBLyUFzRiK5Lr6ehg9GubODR1J36IxdnWlkkeJoWTXhg1+H9/w4aEj6d348b61VWsmIt2c7zjPlsNbYpsYjhs5juLRxZoxFMlxdXV+tjCOFUkjqkyaXDH+x0pyjnPxrUjaXVSARkQkZfPhzXS6zlgWnonoyAqR3FdfH+9lpOBPI5s+XYlhEikxlOzZvx9aW+OfGFZVXSySIyIC1Lf6ig+VU2OcGE4qoflIc+gwRCRDjh2DvXvjXXgmogI0yaTEULIn7oVnIlVVPincvDl0JCISE/Wt9QyzYSyaHNP90fjEcNfxXZzvOB86FBHJgKgiadxnDMEnhnV10NEROhIZCCWGkj1RYhgtPo+rJak9RFpOKiIp9a31lEwqYdTwUaFD6VNJUQkOx/Zj20OHIiIZEFUkTcqMYVsbbNkSOhIZCCWGkj0bNsCcOTBpUuhILq+szBfHUQEaEUlpONRARXG8h+l1ZIVIbktCRdKIKpMmkxJDyZ5Nmy62FHFWWAiLF6s1ExEA2jvb2XJ4S+wTQx1ZIZLb6uqgvDzeFUkj5eVQUKB9hkmTgH+0JCe0t/uCLkviWer9TVSZVERSmo8009HVQfmU8tChXNbUMVMZM2KMCtCI5Kj6+mQsIwV/ZHVZmRLDpFFiKNnR1OSTw6QkhlVVsG0bnDwZOhIRCazhUANA7GcMzUxHVojkqGPHYM+eZBSeiagyafIoMZTsiGbfkpIYRnFGO71FJG9FR1WUTSkLHMmVlUxSYiiSixr8+FRiZgzBJ4Y7d/qkVpJBiaFkx6ZNflF8Wfw7VsDFvZBaTiqS9+pb65k3cR5jCseEDuWKSiaVsO3oNrpcV+hQRCSNonHqpM0Ygko2JIkSQ8mOujooLYVR8S31fol582DMGLVmIkJ9a33sl5FGSopKON95nj0n9oQORUTSqL4errrKd0+SQpVJk0eJoWTHpk3JWv8wbJiPVzOGInmts6uTzYc3UzElGYmhjqwQyU0NDX7RVRIqkkZmzYKJE7XPMEkS9I+XJNbZs9DcnJz9hZGqKg1zieS57ce2c67jHOXF8a5IGomOrFBlUpHc0tiYnN04ETMVoEkaJYaSeY2N0NWVvMRwyRJobYUDB0JHIllmZreZ2WYzazazB3v5/DNmVm9mG83sp2Y2t9tnnWa2PvXzVHYjl3SLCs8kZSnp7AmzGT5suM4yFMkhZ87Ajh3JSwzBJ4a1tb4bKPEXNDFU5ytPJK0iaUQFaPKSmRUADwO3AxXAfWbWMytYB6xwzi0F/h34crfPzjrnqlM/d2UlaMmY6KiKuJ9hGBk+bDjzJs7TUlKRHNLUBM4lNzE8dQq2bw8difRHsMRQna88smkTFBbCwoWhIxkY7ZrOV6uAZufcVudcG/AEcHf3C5xza5xzZ1K/vgLMynKMkiVNh5uYNmYaE0ZNCB1Kv+nIitylAfX81NjoX5OaGIK6UkkRcsZQna98sWmTb81GjAgdycBMnQrFxWrN8s9MYFe333en3uvLbwHPdft9lJnVmNkrZnZPJgKU7Gk52sKCSQtChzEgJZNKaD7SjHMudCiSRhpQz1+NjX6/Xmlp6EgGrrLSx659hskQMjFU5ytfJK0iaXdVVVpKKn0ysw8AK4CvdHt7rnNuBXA/8DUzK+nj3gdSbVhNa2trFqKVwWg52kJJUa//F8bWwqKFnDh/gsNnD4cORdJLA+p5qrHRH1Nx1VWhIxm4sWNhwQIlhkmRiOIzg+18qeMVA2fPws6dyVz/AD4xrKvTrun8sgeY3e33Wan3LmFm7wT+BLjLOXc+et85tyf1uhV4Hrimty9xzj3mnFvhnFtRXFycvuglbc53nGfX8V0XKn0mRelkP63QdLgpcCSSZlkZUFffKX4aG6E8Gduce6XKpMkRMjHMeOdLHa8Y2LrVvyZtf2FkyRI4fRq2bQsdiWTPWqDUzOabWSFwL3DJfhwzuwb4Or5dOtjt/UlmNjL15ynAjUB91iKXtNp+bDsOl7jEMDrLUEdW5K+hrGZQ3yleurpg8+bkjq+DTwybmnx1VYm3kImhOl/5oDnVMUniwnhQZdI85JzrAD4F/BBoAJ50ztWZ2ZfMLNqX8xVgLPBvPQo5lAM1ZrYBWAP8lXNObVNCRQVckraUdP7E+QyzYUoMc09WVjNIvOza5RdfJT0xdM4vwJJ4Gx7qi51zHWYWdb4KgG9EnS+gxjn3FJd2vgB2pjZMlwNfN7MufHKrzldcNaWWMiV1xrAita+/thbuvvvy10rOcM49Czzb473Pd/vzO/u472WgKrPRSbZEZwEmbcZw5PCRzJkwh6YjWkqaYy4MqOMTwnvxs38XdBtQv63ngDpwxjl3vtuAevfCNBJTSa5IGulemXTlyrCxyOUFSwxBna+80NwMkyfDpEmhIxmcceNg/nxVJhXJQy1HWxgzYgxTx0wNHcqALSxaqBnDHKMB9fyUC4nhggUwerT2GSZB0MRQ8kBTU3JnCyOqTCqSl6KKpKkOdqKUFpXynU3fwTmXyPildxpQzz+NjVBUBFOmhI5k8IYN8yUblBjGXyKqkkqCNTcnPzGsrPQ7v9vaQkciIlnUcqQlcctIIwuLFnLs3DGOnD0SOhQRGYLGRj9bmPTxnagyqY5XjbdBJ4ZmNiZ12KpI786d87umk1p4JlJeDp2dFyusikjO63JdbD26NdGJIagyqUjSNTQkexlpZOlSOHwY9u0LHYlcTr8TQzMbZmb3m9kzZnYQaAT2mVm9mX3FzBI+LSRpt3WrHxpK+oxh1CJHC/1FJOftO7mP853nE1eRNFJalDrLUAVoRBLr6FE4cCB3EkPQctK4G8iM4RqgBPhjYLpzbrZzbirwVuAV4K9T5+aIeEk/qiKyeLF/VWKYOGb2H2Z2h5lp2bwMyIWjKhI6Yzh/0nwM04xhjKl9kivZvNm/5kJiGJ3+pVp+8TaQxuidzrk/c85tdM51RW865444577rnHsP8K/pD1ESK0oMkz5jOH48zJihxDCZHsGXc28ys78ys8WhA5JkiI6qWDBpQeBIBmfU8FHMmTBHiWG8qX2Sy8qFiqSRoiKYNUszhnHX78TQOdcOYGZ/Z32UOIuuEQF8RdKiIv+TdOXlSgwTyDn3E+fc+4HlwHbgJ2b2spn9ppmNCBudxFnL0RYKrIA5E+aEDmXQFhYt1FLSGFP7JFfS2AgjRvhTs3JBVZUSw7gbzPKFk8BTZjYGwMxuNbOX0huW5IRcqEgaKSvzO8BVTitxzGwy8BHgt4F1wN/hO2I/DhiWxFzL0RbmTpzLiILk9s91lmH8qX2Sy2ls9LtxhufI4XJLl/qulIq8x9eA/1Fzzn3OzO4HnjezNuAU8GDaI5Pka2qCG28MHUV6lJXBiROwfz9cfXXoaKSfzOx7wGLgW8CvOueiemj/amY14SKTuEvyURWR0qJSjpw9wpGzRyi6KgdWbuQYtU9yJY2N/sSsXLF0KbS3+72TVTpVM5YGPGNoZu8Afgc4DUwBPu2c+0W6A5OEO38edu5MfuGZiCqTJtU/OOcqnHMPRZ0uMxsJ4JxbETY0ibOWo8lPDHVkReypfZI+tbdDS0tu7C+MqDJp/A1mKemfAH/qnLsZeC9+ZGt1WqOS5Nu2LTeOqogoMUyqP+/lvV9mPQpJlOhg+KQeVRFRYhh7ap+kTy0t0NGRW4nh4sV+z6Qqk8bXYJaSru7251ozux34LnBDOgOThGtKFTzIlRnDmTNh7FglhglhZtOBmcBVZnYNEBXMGg+MDhaYJEJUkTTpM4YlRSUYRtNhFaCJE7VP0h+5VJE0MmIEVFRoxjDO+p0Ympk59+bKG865fanlpX1eI3koV46qiJj51lmJYVLcii/oMAv4arf3TwKfDRGQJMeFMwwTPmM4avgoZo2fRfNRzRjGjNonuaJcTAzB7y1csyZ0FNKXgcwYrjGz7wL/5ZzbGb1pZoXA9Wb2YWAN8E/pDVESqbkZJk7MjaMqImVl8MILoaOQfnDOfRP4ppm9xzn33dDxSLIk/QzD7konl2opacyofZL+aGz0i5XGjQsdSXotXQrf/jYcPgyTJ4eORnoaSGJ4G/BR4DtmNh84BowCCoAfAV9zzq1Lf4iSSNFRFb0feZlMZWW+NTt1yi8rldgysw84574NzDOzz/T83Dn31V5uEwH8jOG0MdMYW5j8f88XTlrIdxuUe8SJ2ifpj8bG3JsthIsFaGpr4eabg4YivRjIAffnnHOPOOduBOYC7wCWO+fmOud+R0mhXCKXzjCMRC30li1h45D+GJN6HQuM6+VHpE8tR1sSv4w0srBoIYfPHubo2aOhQ5GL1D7JZTmX+4mh9hnG00D2GBbjN0bvdM61A/uucIvkq7Y22L4d7r8/dCTp1b0y6fLlYWORy3LOfT31+r9CxyLJ03KkhZvn3Rw6jLQonewLgDUfaWblzJWBoxFQ+yRXduAAHD+em4nh9OlQXAwbNoSORHpzxRlDM/uYmX0L+AvgY8A/mdkjqeWkIm+2fTt0deVORdLIwoUwbJgK0CSImX3ZzMab2Qgz+6mZtZrZB0LHJfF1vuM8u0/szon9haAjK+JM7ZP0JVcLz4DfYVRdDevXh45EetOfpaRTnXMfdM494Jz7n8659wP/g0EcdSF5ItcqkkZGjoSSEiWGyfJu59wJ4E5gO7AQ336J9Gr7se04XOKPqohECa4Sw1hS+yS9amjwr7mYGIJPDDdtgvb20JFIT/1JDNvN7He6v+GcO+2c08FI0rtcTQzBt9JRiy1JEA1g3QH8m3PueMhgJP5y5aiKyOgRo5k1fhZNR/Sf7BhS+yS9amyEMWN8VdJcVF3tdx1pnD1+rpgYOuf+Cp8c/q2Zvc3Mkl+mTTKrudnXVy4uDh1J+pWV+eIznZ2hI5H+edrMGoG3AD9N7ZU+FzgmibFcOdy+u4VFCzVjGE9qn6RXUeGZXCrs3l11tX/VctL46c8ew08C9wCbgFXAo5kOShKuqSn3jqqIlJVdLK4jseecexC4AViRKpp1Grg7bFQSZy1HWxgzYgxTx0wNHUralBbpLMM4UvskfcnViqSRRYtg1ChYp/MMYqc/+wT3OefuyXgkkjuam+Gaa0JHkRndK5OW5M6MQo4rw58X1r29++dQwUi8RUdVWA4NbC0sWkjrmVaOnzvOhFETQocjl1L7JJc4fRp27sztxHD4cKiq0oxhHPVnj+Fzvb1pZqPSHIvkgvZ2P5uWaxVJI90TQ4m9VEXlvwHeCqxM/azox323mdlmM2s2swd7+fwzZlZvZhtT1QTndvvsw2bWlPr5cBr/OpIFLUdacmoZKagyaVwNtn2S3BYdlbx4cdg4Mi2qTOpc6Eiku/4khg+Z2VfN7LfN7L1m9j/M7BH8mvghUecrB+3cCR0duVl4BqCoCKZOVWKYHCuAG51zn3TO/V7q59OXu8HMCoCHgduBCuA+M6vocdk6/PKvpcC/A19O3VsEfAG4Fr/0/gtmNimtfyPJmC7XxbZj23IuMSwt8gN1KkATOwNun0B9p1xXX+9fKyvDxpFp1dVw9Cjs2hU6EumuP8Vn/gD4c/yB9sOBNalG7KWhfLE6XzkqlyuSRlSZNEk2AdMHeM8qoNk5t9U51wY8QY99P865Nc65M6lfXwFmpf58K/Bj59wR59xR4MfAbYOOXrJq94ndnOs4d2GGLVdEFVY1Yxg7A26f1HfKfXV1fqllLnej4OKOIy0njZf+zBgC/AHwEXwH53yavludr1wUrYHI5RatrEwzhskxBag3sx+a2VPRzxXumQl0H8PcnXqvL7/FxSX3A71XYiRKnEon59ZS+NEjRjNz3EwlhvEzmPZJfaccV1/vi7MUFoaOJLOqqnyNQiWG8dLfQ+qvcs69z8wKgb8DPpGG7+6tA3XtZa5X5ysJ6upg4kSYPtBJmgQpK4PDh+HQIZgyJXQ0cnlfzOTDzewD+OVgNw3i3geABwDmzJmT5shkMJoO+6WW0dLLXLKwaKGWksbPFwdxj/pOOa6u7uJxDrls7FhfjkKJYbz0d8ZwlJktT41OZb1UW7fO11cGeN8DZlZjZjWtra2ZCU4uVVfnF8bnUEW/N1EBmsRwzr0AbAdGpP68FnjjCrftAWZ3+31W6r1LmNk7gT8B7nLOnR/IvanYHnPOrXDOrSjOxTM/E6jpSBOjho9i5vjc6yvrLMP4GWT71G/qOyXP2bOwdWvu7y+MVFfryIq46W9i+D+A1Wb2DeBKyxz6K+OdL3W8ssy5i4lhLisv969KDGPPzH4Hv8fm66m3ZgL/eYXb1gKlZjY/tUriXnq0e2Z2TeqZdznnDnb76IfAu81sUmrvzrtT70kCNB1pomRSCcOsv/9pTI7SolIOnj7IifMnQociKYNsn9R3ymFbtkBXF1T03DWao6qrfSH7Y8dCRyKR/hxw/35gtnPub5xzH3XOPdvj8z8a5Her85Vr9u/3JaZyPTGcM8efzKrEMAl+F7gROAHgnGsCLntyuXOuA/gUvk1pAJ50ztWZ2ZfM7K7UZV8BxgL/Zmbro31BzrkjwJ/h27e1wJdS70kCNB1uyrn9hREdWRFLA26fUN8pp9XV+ddc70ZFoiWzGzaEjUMu6s8ew1bgkVQDdAjY4pzrXh652cy+BvxP4NeBX3POvedKD3XOdZhZ1PkqAL4Rdb6AGufcU1za+QLY6Zy7yzl3xMyizheo8xUP+dKiDRvmDxhSYpgE551zbdFh5alDpK94alJqAOzZHu99vtuf33mZe78BfGOwAUsYnV2dtBxt4c5Fd4YOJSO6J4bLr14eOBpJGXD7pL5Tbquvh4KC3D0KuqcoMVy/Hm4a8E59yYQrJobOuR+Z2U3OuT8xs3HAQz0u+R5wC7AX+O/Ae/v75ep85Zh8SQzB7zNcu/bK10loL5jZZ4GrzOxdwCeB7weOSWJo14ldtHW25WThGbiYGEYFdiQWBtU+qe+Uu+rqfFKY6xVJI9On+6OhVYAmPvq7kWK8mb0Ff1TFmB6ffQdf8epG4F2AzsTJV3V1/gD4adNCR5J5ZWWwbRucOxc6Erm8B/GrHmqBj+E7U58LGpHE0oWKpDm6lHRM4RhmjJvBliNbQociF6l9kkvU1+fH2HrEzJ9nqAI08dHf4yo+gz+i4neBH3T/wDn3G9GfzewP8Aev3peuACVB8qEiaaS83BfbaWryh/FILDnnuszsP4H/dM6pvJ70KTrKIVdnDAEqiiuoO1gXOgxJUfsk3Z07B83N8Bu/ceVrc0lVFaxZAx0dMLy/WYlkTL9mDJ1z7cBx4C7gUTP759Sy0p7XHQR+O70hSiLkS0XSiI6siDXzvmhmh4DNwGYzazWzz1/pXslPTYebGD1iNDPGzQgdSsZUFlfScKiBLtcVOpS8pvZJehNVJM2XblSkshLa2qClJXQkAv1fSgrwp/ilomXADuAve7vIOXc6DXFJ0uzdC8eP50+LVlrqZ0YbGkJHIr37A/zy9pXOuSLnXBH+EOgbUysbRC7RdKSJhUULsRxe8bBk6hLOtJ9h+7HtoUPJd2qf5E2iMg35clRFJOo21teHjUO8gSSGJ5xz65xzB51zfwqsylRQkkD5VHgGYPRoWLAANm0KHYn07oPAfc65bdEbzrmtwAeADwWLSmIrSgxzWWWxb583HVS7FZjaJ3mTujpfkXTRotCRZFd0NHSdVrnHwkASw6vN7AEze7uZFQMjMhWUJFD0b/SSJWHjyKbqapXSiq8RzrlDPd9M7eNR2yWX6OjqYOvRrTm9vxD8HkNA+wzDU/skb7Jxo9+lMnJk6Eiya+xYmDtXiWFcDCQx/AJQhT+8eTOwxMyeNbOHzEzFZvJdXR0UF/uffFFd7XeKnzwZOhJ5s7ZBfiZ5aMexHXR0deR8Yjhh1ARmjZ9FXat6YIGpfZI32bgRli4NHUUYlZVaShoX/a7/45x7rPvvZjYLnyguBX4Ff2yF5KtNm/JnGWlk2TJfdKe2Fm64IXQ0cqllZnail/cNGJXtYCTethz2Rzjk6lEV3S2ZukSJYXhqn+QSx4/Djh3w8Y+HjiSMigr4yU9UmTQOBv0/v3NuN7Abf4ah5DPn/FDPh/Jsa0R1tX9dv16JYcw45wpCxyDJ0XDIF5GKllrmssriStZsW0NnVycFw/SvSQhqn6SnqFxBvp5+FVUm3bo1//ZYxs1AlpKK9G7XLr+cMt9mDGfNgqIi7TMUSbj61nqKRxczZfSU0KFkXGVxJec7z9NyVLXhReJi40b/ms9LSUH7DONAiaEMXb5VJI2Y+VnDDRtCRyIiQ9BwqIHy4vLQYWRF5VTfTqsAjUh8bNwIEyf68eZ8pMqk8aHEUIYuXxND8Inhxo1+YbyIJI5zjvrWeiqm5P4yUuhWmVT7DEViIyo8k8PHqF5WVJlUBWjCU2IoQ1dXB9OmweTJoSPJvupqOHcOmppCRyIig7D/1H6OnTuWF/sLAcYWjmXexHk6y1AkJqIadvm6jDRSWakZwzhQYihDV1eXn7OFcGkBGhFJnPpWP0SdL4kh+H2GmjEUiYcdO3yZhnwtPBOpqIDNm7UAKzQlhjI0XV1+7j9fE8OyMigsVGIoklBRRdJ82WMI/siKzYc2097ZHjoUkbyX74VnIpWVcP68r0wq4SgxlKHZuRNOn87fxHDECFiyRImhSELVt9YzYeQErh57dehQsqayuJL2rnaajmgJvEhoUWK4ZEnYOEKLCtA0NISNI98pMZShyefCM5Fly2DdOr9RQEQSpb61noriCiyPqj6oMqlIfNTWQkmJL8CSz8rK/KsSw7CUGMrQKDH0+wxbW2H//tCRiMgANRxqyKv9hQBlU8owTPsMRWJg40btLwSYMAFmzFBiGJoSQxmaujq4+mqYNCl0JOGoAI1IIh06c4iDpw9SPiV/9hcCjB4xmpKiEiWGIoGdPQtbtmh/YaS8XIlhaEoMZWjq6rQwftky/6rEUCRRGlp9DyTfZgzB7zPUkRUiYdXX+xp+Sgy98nJobNTOnJCUGMrgdXbmd0XSyIQJMH++EkORhMnHoyoilcWVNB1u4nzH+dChiOQtVSS9VHm5P7pjz57QkeQvJYYyeFu3+nUQWhzvl5MqMRRJlLrWOsaMGMPsCbNDh5J1lVMr6XSdbDm8JXQoInmrthZGj4YFC0JHEg+qTBqeEkMZvNpa/5rvS0nBJ4ZNTf7oDkk8M7vNzDabWbOZPdjL5283szfMrMPM3tvjs04zW5/6eSp7UctA1R6spWpaFcMs//5TuGSqb7e1z1AknI0b/aKrgoLQkcRDlBg2NoaNI58F/a+hOl8Jt2kTmGkpKfjE0LmLybIklpkVAA8DtwMVwH1m1nOt4U7gI8DjvTzirHOuOvVzV0aDlUFzzrHxwEaqpubniofFkxdTYAXaZ5gw6jflDudgwwYtI+1u2jSYOFEzhiEND/XF3Tpf7wJ2A2vN7CnnXH23y6LO13/v5RFnnXPVGQ9U+lZb69c/jBkTOpLwulcmve66sLHIUK0Cmp1zWwHM7AngbuBC2+Sc2576rCtEgDJ0+07t48jZIyydlp+9spHDR7KwaKFmDBNE/abccuAAHDqkxLA7M1UmDS3kjOGFzpdzrg2IOl8XOOe2O+c2Aup8xVFtrfYXRmbP9kd2aJ9hLpgJ7Or2++7Ue/01ysxqzOwVM7snvaFJumw84Ks+5OuMIfh9hjrkPlHUb8oh0QIjJYaXUmIYVsjEUJ2vJDt71u+p0/5Cz8wfW6HEUGCuc24FcD/wNTMr6e0iM3sg1YbVtLa2ZjdCofaA75VVTcvfxHBJ8RJajrZwtv1s6FCkf9RvyiFRRVKNr1+qvNzPph49GjqS/JTkHfdX7Hyp45VBjY3+8B21aBdVV/uWvrMzdCQyNHuA7mUqZ6Xe6xfn3J7U61bgeeCaPq57zDm3wjm3ori4ePDRyqDUHqxl5riZFF1VFDqUYJZMXUKX66LhkIbn84QGrWJk40aYMQMmTw4dSbyoMmlYIRPDjHe+1PHKoGgNhBLDi6qrL86kSpKtBUrNbL6ZFQL3Av0q1GBmk8xsZOrPU4Ab6bY3UeJj44GNeT1bCBdnS6PZU4k9DVrlkI0btYy0N0oMwwqZGKrzlWS1tVBYCKWloSOJj+4FaCSxnHMdwKeAHwINwJPOuToz+5KZ3QVgZivNbDfwPuDrZhZt1CoHasxsA7AG+KsehSEkBto722k41MDSqfndK1tYtJBRw0dd2G8psad+U45ob4f6eo2t92buXBg1SolhKMGqkjrnOsws6nwVAN+IOl9AjXPuKTNbCXwPmAT8qpn9L+dcJb7z9fVURcBhqPOVfbW1flhneLB/hOKnvBxGjPCJ4b33ho5GhsA59yzwbI/3Pt/tz2vxo/U973sZ0H/qY67pSBNtnW15P2M4fNhwKoorqD2oGcMkUL8pd9TXQ1sbXNPrnG1+KyiAxYuVGIYStFevzleCbdoEt9wSOop4KSz0ZzpqxlAk1qIZsnw9qqK7qqlV/LDlh6HDkH5Svyk3rFvnX5UY9q68HF59NXQU+SnJxWcklKNHYc8erYHoTXW1EkORmKs9UMvwYcMpm1IWOpTglk5byv5T+2k9rSIjItmybh2MHq3dOH0pL4ftwc3ISQAAIABJREFU233ZBskuJYYycFHio13Tb1Zd7ess798fOhIR6UPtwVoWT15MYUFh6FCCi85x1HJSkexZt86fcFVQEDqSeCovB+dg8+bQkeQfJYYycDU1/nXFirBxxFFUgGbDhrBxiEif1u1fx7Lpy0KHEQvRclpVJhXJjq4uP76uZaR9U2XScJQYysC9/jrMmwdTpoSOJH6WpTqbWk4qEkutp1vZfWI3b7n6LaFDiYVpY6dRPLpYlUlFsmTrVjh5Uonh5ZSW+tnUepVHyjolhjJwNTXwFnWqejVxoq+1rMRQJJbW7fdVH66Zrl5ZpGpalZaSimSJCs9c2ciRsGiRP+tRskuJoQzM0aPQ0qJlpJejAjQisfXGvjcAuOZq9coiS6cupa61js6uztChiOS8dev8SV9LloSOJN6WLdOunBCUGMrAvP66f1Vi2Lfqar9j+vTp0JGISA/r9q9j/sT5TBw1MXQosVE1rYoz7WfYenRr6FBEct66dVBR4WfFpG9Ll8KOHXD8eOhI8osSQxmYX/wChg2Da68NHUl8VVf7clqbNoWORER6eGPfGyy/ennoMGIlKkCjfYYimbdunZaR9kdUskHLSbNLiaEMzAsvwPLlMG5c6EjiK6pMquWkIrFy/Nxxmo80KzHsYcnUJQwfNpyavTWhQxHJafv2+ROtlBheWZQYajlpdikxlP47fx5eeQXe/vbQkcTb3LkwYYISQ5GY2XDA9zBUeOZSo4aPYum0pazduzZ0KCI5LdqNo8TwymbMgMmT1ZXKNiWG0n9r1/rk8KabQkcSb2YqQCMSQ1HhGc0YvtnKGSup2VtDl+sKHYpIzlq71u/GWa4m6IrM/P9OUTIt2aHEUPrvhRf861vfGjaOJKiu9gvjO1XlTyQu3tj3BlePvZppY6eFDiV2Vs1cxfHzx2k63BQ6FJGcVVPjD28fOzZ0JMmwahXU1sKZM6EjyR9KDKX/fv5zqKqCoqLQkcRfdbVvyZqbQ0ciIinr9q/TbGEfVs5YCaDlpCIZ4pyfMVy5MnQkybFypR9f1wKs7FFiKP3T0QEvvaT9hf2lAjQisXKm/QwNrQ1KDPtQXlzO6BGjWbtHiaFIJuzcCa2tOu1rIFat8q9r1SxljRJD6Z916/y5fNpf2D8VFVBYCG+8EToSEQFe3/s6na6TVTNXhQ4lloYPG87yq5drxlAkQ2pSRX81Y9h/V18NM2fCa6+FjiR/KDGU/on2F77tbWHjSIrCQn86a43Kv4vEwat7XgXg2pk6g7UvK2esZN3+dbR3tocORSTnrF0LI0ZcPIZB+ue66/yCNckOJYbSPz//OSxaBNOnh44kOVas8OW0ulTlTyS0V/e8yvyJ8ykeUxw6lNhaNXMV5zrOsengptChiOSctWt9mYaRI0NHkiw33ww7dsD27aEjyQ9KDOXKurrgF7/Q/sKBWrECjh+HlpbQkYjkvVd3v6plpFegAjQimdHV5ceJtYx04G6+2b8+/3zIKPKHEkO5stpaOHZM+wsHKtphrl3TIkHtO7mPXSd2aRnpFSyYtICiq4p4bY829IikU3OzHydWYjhwlZUwZQqsWRM6kvygxFCu7Oc/96+aMRyYigoYNUr7DEUCu7C/cJYSw8sxM1bNXKXEUCTNovFhVSQdODM/a/j88/7ID8ksJYZyZT//OcydC3PmhI4kWUaMgGuuUWIoEtiru19l+LDhXDP9mtChxN61M6+lrrWOU22nQocikjNefRVGj/azXzJwN9/sj/vQPsPMU2Iol+ecTwy1jHRwVqzwR1Z0doaORCRvvbrnVZZNW8ZVI64KHUrsrZq5ii7XRc1eDWiJpMsvf+mXkQ4fHjqSZLrlFv+q5aSZp8RQLm/zZjh4UMtIB2vFCn/+4+bNoSMRyUudXZ2s3btW+wv7KSrQ8+ruVwNHIpIbzp6F9evh+utDR5Jc5eVQXKwCNNkQNDE0s9vMbLOZNZvZg718/nYze8PMOszsvT0++7CZNaV+Ppy9qPOM9hcOjQrQJJLaptzRcKiBU22ntL+wn6aMnkLJpJIL+zIlftQ+JUtNDXR0KDEcimif4Zo12meYacESQzMrAB4GbgcqgPvMrKLHZTuBjwCP97i3CPgCcC2wCviCmU3KdMx56YUX/NmFCxeGjiSZFi+GMWO0zzBB1Dblll/u+iUA1826LnAkyXHtrGuVGMaU2qfk+aVvgrhOTdCQrF4Nu3fDli2hI8ltIWcMVwHNzrmtzrk24Ang7u4XOOe2O+c2Aj1PCL8V+LFz7ohz7ijwY+C2bASdV5zzieFNN/nhGhm4ggJ4y1uUGCaL2qYc8vLul5kyegqlRaWhQ0mMa2dey96Te9l9YnfoUOTN1D4lzC9/CSUlMHVq6EiS7dZb/esPfhA2jlwXMjGcCezq9vvu1HuZvlf6a/t22LNHy0iHasUKv8GgvT10JNI/aptyyMu7XuaG2TdgGtzqt2g/pvYZxpLapwRxzieGWkY6dPPn+0VYSgwzK6eLz5jZA2b/v737Do+yyt8//j4JSSD0EimRKqhBkGIoGqQqoKuoKK6Aa8EF/apr25+uqKte9l1X3XXXtopYFgsoKnYgVCmuVDVBEUQEQQgt1CBJzu+PM1liBEmZ5Mwzc7+85ppkMjH3JOGT5/M8p5hFxphFOTk5vuMEz+zZ7l6NYcWkp0NeHmRl+U4iEUT1qfLl7Mlh5daVnHL0Kb6jBErnJp1JjE/UcNIYpdoUPt99B5s2wSkqQWExaJA7NN23z3eS6OWzMfwBaF7s/aNDj4Xtc621/7bWpltr01NSUsodNGbNmQMNGriN2qX8ihag0XDSoKj02gSqT1VhwXo3uSejRYbnJMGSVC2Jzk06a6P7yKRjpwApml+oK4bhMXiwawrnzvWdJHr5bAw/A9oZY1obYxKBi4Appfzcj4GBxpj6oYnTA0OPSTjNmeOuFsZF9YXlynfMMVC3rhrD4FBtihLz180nIS6Bk5qe5DtK4PRI7cGiDYsoKNQerBFG9SlAFixw68916OA7SXTo0weSkjSctDJ5O+K31uYD1+KK0gpgorU2yxhzjzFmCIAxppsxZj0wDHjGGJMV+txtwL24AvkZcE/oMQmXH36A1as1jDQc4uLcVcP/6ux7EKg2RY/56+bTtWlXbWxfDj1Se7DnwB6ycjQEPpKoPgXLJ59Ajx7a2D5ckpNdc6jGsPJ4/VW11n4AfFDisTuLvf0ZbqjDoT73eeD5Sg0Yy7R/YXj17AkPPQS7d0OtWr7TyBGoNgXfTwU/8dmGz7g6/WrfUQKpaN/HT9d/yomNT/ScRopTfQqG7dth+XK4+27fSaLL4MFw003w/ffQooXvNNFHYwTl0ObMgdq1oVMn30miQ0YGFBToqqFIFVm6cSl5+Xmc0lyrPpTHMfWPoUGNBlqARqScPvnErUrap4/vJNGlaNuKjzUIulKoMZRDmzMHevXS+IdwOflktxfkvHm+k4jEhPnr5gNwcnOt+lAexhi6p3ZXYyhSTrNnQ2KiG0oq4ZOWBs2bazhpZVFjKL+UkwPZ2RpGGk716sEJJ6gxFKki89fPp1W9VjSr3cx3lMDqkdqDrM1Z7Nq/y3cUkcCZPds1hdWr+04SXYxxw0mnT9f20JVBjaH8UtE6wGoMwysjwy1RVljoO4lIVLPWMu/7eWQ01zYVFdEjtQcWy6INWlFZpCx27oQlSzSMtLIMHuy+xwsX+k4SfdQYyi/NmQM1ahzcf0/CIyPDVTJtdC9SqdbmrmXj7o2aX1hB3VO7A2g4qUgZzZvnzgGrMawcAwZAfLzmGVYGNYbyS7NnuzlxiYm+k0SXU0IHqRpOKlKpiuYXqjGsmIbJDWnboK02uhcpo9mz3RIN2ti+ctSt6763mmcYfmoM5ed27HDrK2sYafi1aQONG6sxFKlk876fR63EWnQ4SrtKV1SP1B66YihSRrNnQ7dubnN7qRyDB8PixbB5s+8k0UWNofzc3LlaX7myGOOGk6oxFKlUM76bQa8WvagWp1WVK6pHag827NrA+p3rfUcRCYRdu2DRIujb13eS6DZ4sLufOtVvjmijxlB+bsYMt4RWz56+k0SnXr1gzRpYr4MskcqwYdcGvtryFQNaD/AdJSoU3+heRI5s1izIz4fTT/edJLp16QIpKRpOGm5qDOXnZs50c+G0vnLlOO00dz9tmt8cIlFqxpoZAGoMw6RT404kxidqOKlIKU2dCsnJB5cVkMoRF+c2u586VYu9h5MaQzlo61Y3v7BfP99JoleHDtCkicY+iFSSzDWZNKjRgE5NOvmOEhWSqiXRpUkXNYYipTR1qpuNk5TkO0n0GzTIbb29dKnvJNFDjaEcNGuWu+/f32uMqGYMDBzorhjqFJdIWFlryfw2k36t+hFn9OctXHqk9mDRhkXkF+b7jiIS0dauhZUr3Z95qXxF32cNJw0f/eWUg2bOdEtodevmO0l0GzjQXZ1dpE2jRcJp9fbVrNu5TsNIw6x7anf2HtjLl5u/9B1FJKIVzRLR/MKqcdRRcNJJagzDSY2hHDRzJpx6KiQk+E4S3c44w21w9NZbvpOIRJXMbzMBGNBGjWE49W7pti+auWam5yQikW3aNGjWDNq3950kdgweDAsWQG6u7yTRQY2hOD/+CNnZml9YFRo0cN/nN990W4OISFhkrskktXYq7Rq08x0lqjSv25zjGh7H9DXTfUcRiVgFBTB9urtaaIzvNLFj8GD3vc/M9J0kOqgxFEfzC6vW0KHwzTeuGReRCssvzCdzTSYD2gzA6Kgs7Aa0HsDs72bzU8FPvqOIRKTFi2HbNg0jrWo9ekCdOhpOGi5qDMX56CN3JatLF99JYsO557pTim++6TuJSFRYsG4B2/Zt46x2Z/mOEpVOa3Maew7sYeH6hb6jiESkd96B+Hg3W0SqTkKC2wnso480CCsc1BiKWx3zww/dur/x8b7TxIYmTSAjAyZP9p1EJCq8u/JdEuISGNR2kO8oUal/6/4kxCXw3sr3fEcRiUhvvw29e7tz7FK1Bg+GdetgxQrfSYJPjaG4DWA2b4Yzz/SdJLYMHer2jVy92ncSkcB7d+W79GnVhzpJdXxHiUp1q9elf+v+TF4xGavT8iI/UzQz5NxzfSeJTYNC5wM//thvjmigxlDggw/csMZBOtNepYYOdfdvvOE3h0jArchZwVdbvmLIsUN8R4lqQ9OGsnr7am1bIVLCpEnu/pxz/OaIVS1aQFqaG/wmFaPGUNy/pG7dICXFd5LY0rIl9OwJr77qO4lIoE3KnoTBcH77831HiWrnHHcOBsPkFRoCL1LEWpgwwc0OadnSd5rY9ZvfuHUUt23znSTY1BjGuq1bYeFCzZb2ZeRIN5w0K8t3EpHAmpg1kVNbnkqz2s18R4lqjWs1JqNFBm99pT1YRYosX+6GkY4c6TtJbBs+HA4c0CCsilJjGOumTnWnuzS/0I9hw9yCP7pqKFIu2TnZZOVkMaz9MN9RYsJ5x5/H8k3L+Xb7t76jiESECROgWjX351z86dIFjj8eXnnFd5JgU2MY695/Hxo1gvR030liU+PGbp3lV17ROssRxBgz2BjztTFmlTHm1kN8PMkY83ro458aY1qFHm9ljNlnjFkWuj1d1dljzaSs0DDSNA0jrQrnHX8egIaTiuA2Vn/1VTfoqlEj32limzEwYgTMnu1WKJXy8doY6uDLs/374d13YcgQiNM5Am9GjIA1a9yQXvHOGBMPPAGcAbQHhhtj2pd42hXAdmttW+Ax4C/FPrbaWts5dLuqSkLHsInZE+ndsjdNazf1HSUmtK7fmvRm6fzn8//4jhKzdOwUOebMgR9+0DDSSDF8uLt/7TW/OYLMWzegg68IMG0a7Nyp8Q++nXsuVK+u8Q+Rozuwylr7rbX2J+A1oORac+cAL4befgMYYIwxVZhRgKzNWWTnZHPhCRf6jhJTLut0Gcs3LWfpxqW+o8QcHTtFlgkToFYtOPts30kEoG1b6N5dh1MV4fMykQ6+fJs0CerVg/79fSeJbXXquL8qr78O+fm+0wikAsUHoqwPPXbI51hr84FcoGHoY62NMUuNMbONMadWdthYNjFrIgbD0LShvqPElOEdh5MUn8TzS5/3HSUW6dgpQuTluYVOhg6F5GTfaaTIyJGwbBl8qV11ysVnY1jpB1/GmDHGmEXGmEU5OTnhTR90e/bA5MmuoiUm+k4jI0ZATg5kZvpOIhWzEWhhre0C3AS8Yow55I7rqk8VY61lUvYk+rTqQ5NaTXzHiSkNajTgvLTzmPDFBPLy83zHiTU6cRUhPvgAcnM1jDTSDB8OCQkwfrzvJMEU1IllpTr4stb+21qbbq1NT9EefT83eTLs3g2XXeY7iYCbuV63rhuXIr79ADQv9v7RoccO+RxjTDWgLrDVWrvfWrsVwFq7GFgNHHuoL6L6VDFZOVms2LKCC9trGKkPl3e+nO1525ny9RTfUaT0SnXspJNWpfOf/7j14zToKrKkpLilM156CX76yXea4PHZGFbJwZccxvjx0KYN9OrlO4kAJCXBhRfCm2/Cjh2+08S6z4B2xpjWxphE4CKg5NHvFODS0NsXADOstdYYkxKaA4Qxpg3QDtC6/pVgwucTiDfxGkbqyYDWA2hepznjlo7zHSXWVPqxk05aHdmmTW7tvosvdltVSGQZNQq2bIH33vOdJHh8NoY6+PJlxQqYOROuuMKt7yuR4corYe9edxpSvAkNvboW+BhYAUy01mYZY+4xxgwJPW0c0NAYswp35r1oZcDewOfGmGW4uT1XWWu3Ve0riH4FhQW89PlLDG47mMa1GvuOE5Pi4+IZ3XU0U1dP5cvNmsxThXTsFAFeftktCXDFFb6TyKEMHAjNmsHzmgZdZt4aQx18efT44+4K1ejRvpNIcSedBN26wVNPaU9Dz6y1H1hrj7XWHmOtvT/02J3W2imht/OstcOstW2ttd2ttd+GHn/TWntCaMW/rtbad32+jmiVuSaTDbs2cFnny3xHiWlXd7uamgk1+eu8v/qOEjN07OSftTBuHJx8MqSl+U4jh1KtGlx6KXz4IWzY4DtNsHidY6iDLw+2bHEDr0eMcAOxJbL84Q+Qne1mtYvIIb2w7AXqV6/P2cdqjXifGiY3ZHTX0bzyxSus3bHWd5yYoWMnvxYsgK++0tXCSHf55VBY6A55pfSCuviMlNejj8K+fXDzzb6TyKFcdBG0bAkPPqirhiKHkJuXy1tfvcXwDsNJqpbkO07Mu+nkmzDG8OiCR31HEakS48ZBzZpuWQCJXO3awamnuuGkOpwqPTWGsWTrVvjnP1010/iHyJSQ4Jr2efNg6lTfaUQizsSsieTl52kYaYRoXrc5IzqO4Lmlz7F5z2bfcUQq1fbtbsvh3/4Watf2nUaO5Ior4Jtv3CGVlI4aw1jy2GNui4o77vCdRH7N6NFuxdibb4aCAt9pRCKGtZYnFz3JCSknkN4s3XccCbmt123sz9/PfXPu8x1FpFI984zbBvq663wnkdK44AKoVUuL0JSFGsNYsX27W3TmggugQwffaeTXJCa6oaRffAH/+pfvNCIRY9Z3s1j24zJu6HkDRisqR4zjGh3H77v+nqcXPc3qbat9xxGpFHl57jBq4EDo1Ml3GimNmjXdDJ2JE2HXLt9pgkGNYaz4+9/dv4o//9l3EimNYcPcpve33QbfajVxEYCH5z9MSnIKIzuO9B1FSrirz10kxCdwx0yNSJHo9NRTsHEj3HrrkZ8rkWPUKHeVd+JE30mCQY1hLNixA/7xDzjvPDjxRN9ppDSMcWNW4uPd0FLNnJYYN+/7eXy46kNuOvkmaiTU8B1HSmhauyk39ryR1758jUUbFvmOIxJWublw//3uamG/fr7TSFn07Ant27sBWDqUOjI1hrHgscdcVbvzTt9JpCyaN4e//Q1mzHBNokiMstYyNnMsTWo14Q/d/+A7jhzGLRm30LhmY65+/2oKCjU/WqLH2LFuRs6DD/pOImVlDPzxj7BsGWRm+k4T+dQYRrucHLdFxQUXQOfOvtNIWY0eDaed5qraqlW+04h4MXX1VOZ+P5c7Tr2Dmok1fceRw6iTVIdHBj7CZxs+49klz/qOIxIW8+a5YaTXXQddu/pOI+UxciQ0bequ+uqq4a9TYxjtHnwQ9u6Fe+/1nUTKwxgYP94tSHPJJZCf7zuRSJUqtIXcNuM2WtVrxeiTRvuOI0cwouMI+rbqy9jMsdq+QgJv/34YMwZatNBhVJAlJbklG2bNgvff950msqkxjGbr1sGTT8Kll8Lxx/tOI+V19NHwxBOwYAH89a++04hUqZeWv8SSjUu4t9+9JMYn+o4jR2CM4ckzn2T3T7u56eObfMcRqZB77oHsbHfFsFYt32mkIq68Eo491g3A2rfPd5rIpcYwmv35z+6a+V13+U4iFTV8uNtR9667YMkS32lEqsTO/Tu5dfqt9Dy6JyM6jvAdR0opLSWN23rdxoQvJjDl6ym+44iUy/TpbtDVFVfAmWf6TiMVlZDgFqBZuVIL9P8aNYbRas4cePFFuOEGaNnSdxqpKGPc1d+jjoLf/c5tqCQS5e6dfS+b9mzi8cGPE2f05ypIbu99Ox2P6siV713Jtn3bfMcRKZNNm+DiiyEtze1dKNHh9NPh//4PHnkE3n7bd5rIpL+00WjnTvj9711DqJVIo0eDBvDcc25cy913+04jUqmyc7L5+6d/Z1TnUXRL7eY7jpRRYnwiL5z7Ajl7crjx4xt9xxEptf373QCd3Fx4/XVITvadSMLpkUege3fX+H/+ue80kUeNYbQpLHRN4erV8NJLUFMr+EWVM85w41oefhgWLvSdRqRSHCg4wCVvXULdpLo8MOAB33GknLo27crYXmN5aflLvL9SKz5I5LPW/YmdPdudh+3QwXciCbcaNdzVwrp1YcgQ+PFH34kiixrDaFJQANdcA5MmwV/+Ar17+04kleHRRyE11S0qtGeP7zQiYTc2cyyLNy7m6bOepnGtxr7jSAXc0fsOOhzVgTHvjWFH3g7fcUR+1R13wIQJbluDkSN9p5HK0rQpvPMObNkC/fu7ocPiqDGMFtu3w9lnw9NPw5/+5JZdkuhUpw688AJ88w1ce63vNCJh9fLyl3lkwSNc0+0aLmh/ge84UkFJ1ZIYf854Nu3epFVKJaLddx888IDbPnjsWN9ppLKlp8MHH8DatTBgAGzW7jqAGsPokJXlBkxPn+4aw4cecouVSPTq39/NH33hBfjHP3ynEQmL91e+z6gpo+jXqh+PDXrMdxwJk/Rm6fwp40+MXzaeF5e96DuOyC/cd59bqfJ3v3NbU+gQKjb07g3vvQfffgu9ern7WKfGMOimTIGePWHXLpg5023UIrHhzjth6FC48UbXIIoE2JvZb3Le6+dxYuMTefuit0mIT/AdScLo7r530791f8a8N4apq6f6jiMCuDmFY8cebArHj4f4eN+ppCr16wfTprlhpaecoh3B1BgGlbVus/Nzz3XrKS9eDBkZvlNJVYqLg5dfdmMgLr/cLUgjEkDjl47nwjcupFtqNzIvyaROUh3fkSTMEuITmDRsEmmN0hjy6hAmZU3yHUliXH4+jBnjBlldeaWawliWkQHz5kFSEvTpA1Nj+NyVGsMg2r8fRo1ycwmHDXPLZ6Wm+k4lPiQnu3EQF14It9zi/sppQRoJiH0H9nHVe1cxasoo+rfuz9SLp1Kvej3fsaSSNKjRgMxLMunatCsXvnEhd8y4g0Jb6DuWxKBNm9wi38895xaceeopNYWxLi0NFiyAY45xvxsPP+yuwcQaNYZB8+OP7rr3Cy/AXXfBq6+6tXcldiUlwSuvuBMFzz0HXbq46iYSwZZuXErPcT15ZvEz3HLKLXww4gNqJmp7nWjXMLkhMy+dyRVdruD+ufdzxoQz2Lhro+9YEkOmTYPOneGTT2DcOLj3Xs0pFKdZM5g7F84/351rHzYMtm71napqqTEMCmvh3Xeha1dYtgwmTnSbnMfpRyi4U50PPQQzZrgryqecAsOHw5o1vpOJ/MzeA3u5ZdotdHu2G5t2b+L9Ee/zl9P/ojmFMSSpWhLPnv0sz5z1DHPXzqXjUx15I/sNbCyenpcqs3q1m5Y/cKBb3PvTT93gK5HiateG11+Hv/3NbWlx/PHu6uGuXb6TVQ11FZFu1y63L2Hfvm4nzoYNYf58dxpDpKS+feHLL91M+nfegXbt3O/KrFlQqCFb4k+hLWTyisl0fKojD89/mMs7X86Ka1ZwZrszfUcTD4wxjDlpDEuuXELLei0ZNmkY/V7sx5Svp7A/f7/veBIl8vPdgu1Dh8Kxx7q5Y/ffD8uXw4kn+k4nkcoYt+vbkiXQqZO7etiiBVx/PSxcGN1DTL02hsaYwcaYr40xq4wxtx7i40nGmNdDH//UGNOq2MfGhh7/2hgzqCpzV5rcXPcb9/zzcPPNbgZsgwZu/tiaNfD447BokRsDIXI4tWvDPfe4fQ5vuAEyM93w46OPhquugo8+grw83ykjmmpT+GzavYlxS8bR6elOnD/xfBLiEphxyQyeHfIs9WvU9x1PPDu+0fF8+vtP+ecZ/+Sbbd9wzmvn0OjhRgybNIyXl7/M1r0xNo6rFFSfDq+wED7/HP71LzccsFEjOP10mDPHHVatXAm33QbVq/tOKkHQsaM7sfDf/7rfo2eegZNPdvMQb7/dnYePNsbX0A1jTDywEjgdWA98Bgy31mYXe87VwInW2quMMRcB51lrf2uMaQ+8CnQHmgHTgWOttQWH+3rp6el20aJFlfeCyiI/31WnZctcBVu+3N1v2HDwOUlJ0KEDnHYaDBrkNlvRzGgpj7174a234O234cMP3eI0CQnuBEPXrtC2rbsdcwy0aQM1gzPPyxiz2FqbHub/Z5XWJoiw+lRO1lo279nMii0ryNqcxfJNy1m8cTFLNy7FYklrlMajJfmdAAAJoklEQVTtp97Obzv8lmpx1XzHlQh0oOAAU1dP5d2V7zLl6yls3L2ROBNHRvMMTm9zOt1Tu9OlaRdSklMwAZgUFg31KZJr04EDsG4dZGe7A/T58928we3b3cdbtHDDRgcNgrPOUjMoFZeb6w6lXnnFnXMvKID27d1grYwMt4BNq1ZQP8LPef5abfLZGJ4M3G2tHRR6fyyAtfbBYs/5OPScBcaYasCPQApwa/HnFn/e4b5euYubte4UVEGBa+jy893bRd83aw/e8vPd/K7it7w8t2DMDz+46rVsGXzxxcErNgkJ7reqY0fXCKalufdbt1YjKOGXl+fmIc6d665Of/45bNv28+c0beqaxKJb27buL2ytWq5prFnT/W7GxbmbMaW/L7qFSSUdeFVpbYLwH3xZa7FYCm1hmd4uKCxgf8F+8vLzfnHbd2Afew/sJXd/Lrl5uezI2+Fu+3fwfe73ZOdks23fwd+lBjUa0LlJZ/q27MvZx51Np8adAnEwL5Gh0BayZOMSpnw9hSlfT2H5puX/+1hyQjIt67akZb2WNK7ZmJTkFFJqppCSnEL9GvVJTkimZkJNkhOS/3erFleN+Lh44kwc8SZ0f5j3wyUa6lO4alPxQ6XCQncrenvvXti929127fr5fcnHcnJg7Vr4/nt3WFV8hkS7du4cetGtZUstKiOVZ/NmN9PrnXfcen+7dx/8WN267jC+RQt3SNW0KTRu7A6fqld3t8REd0tI+Pmt5GPVqrlb8beLDqnK69dqk8/TtqnAumLvrwd6HO451tp8Y0wu0DD0+MISnxue/RpmzXKnloo3geHSoIG7SnP11e6+Uyc3qzUxMXxfQ+TXVK8OZ57pbkW2b3ez8otuq1a5++nT4cUXKyfHkRrHzZvdVhx+RGZtAro804WVW1cescGrCvEmnvo16lOvej2a1mrKsPbDSGuURvuU9qSlpJFaO1WNoJRbnIkjvVk66c3SuaffPeTm5bJ442K+3Pwla3es5bvc71i7Yy1Zm7PI2ZtDXn74hscXbxbjTNz/fo8NhgcGPMB1Pa4L29cqh4isT0884RbGLtn0Fb1d0WsQxrhZEg0buoavXz9336KFO59+wglQTzvdSBU66ii45hp3y8+HrCx36LRmjbt99527nz8ftmwJ/9cvahSL1qBs08ad66+oqB7PY4wZA4wJvbvbGPN1JXyZRkDpfuTbtrmrNTNmVEKMCin9a4hceg2RoXSvoeg07+FOvJR+OGvL0j4x0lRRfSqrUv8OFlDAltB/q1jFXOZWcrRfFeR/O0HNHrW5C0P/Hcr1t1/P9Vxf2q8VyPpUhbWp1L9D1sLOne4WgYttB/XfQkl6HZHlV1/HgQPuVuSLL8p0FfGwtclnY/gD0LzY+0eHHjvUc9aHhkPUBbaW8nOx1v4b+HcYM/+CMWZRuIeKVDW9hsig1xAxKr02QdXUp7IK6s8vqLkhuNmV25uoOHaCqPhZAHodkUavo2J8rkr6GdDOGNPaGJMIXARMKfGcKcClobcvAGZYNylyCnBRaOWt1kA74L9VlFtEoptqk4hEKtUnEak03q4Yhsa9Xwt8DMQDz1trs4wx9wCLrLVTgHHAy8aYVcA2XAEk9LyJQDaQD1xzpFX/RERKQ7VJRCKV6pOIVCZvq5JGC2PMmNCwi8DSa4gMeg3iW1B/fkHNDcHNrtxSUdHys9DriCx6HRX8umoMRUREREREYpvPOYYiIiIiIiISAdQYhpEx5o/GGGuMaeQ7S1kZYx42xnxljPncGPOWMSYQOwIZYwYbY742xqwyxtzqO09ZGWOaG2NmGmOyjTFZxphSr4MeaYwx8caYpcaY93xnkYoLWj0LWg0Lau0Kes1SnYpMQas3JQWt/pQU1HpUXNBrU3E+65QawzAxxjQHBgLf+85STtOADtbaE4GVwFjPeY7IGBMPPAGcAbQHhhtj2vtNVWb5wB+tte2BnsA1AXwNRa4HVvgOIRUX0HoWmBoW8NoV9JqlOhVhAlpvSgpM/Skp4PWouKDXpuK81Sk1huHzGHALEMhJm9baqdba/NC7C3H7G0W67sAqa+231tqfgNeAczxnKhNr7UZr7ZLQ27twhSDVb6qyM8YcDfwGeM53FgmLwNWzgNWwwNauINcs1amIFbh6U1LA6k9Jga1HxQW5NhXnu06pMQwDY8w5wA/W2uW+s4TJKOBD3yFKIRVYV+z99QSwCBQxxrQCugCf+k1SLn/H/WEv9B1EKiZK6lmk17CoqF0BrFmqUxEmSupNSZFef0qKinpUXABrU3Fe65S3fQyDxhgzHWhyiA/dDtyGGwYR0X7tNVhr3wk953bc5fgJVZkt1hljagFvAjdYa3f6zlMWxpizgM3W2sXGmL6+88iRBbWeqYZFjqDVLNUpf4Jab0pS/QmGoNWm4iKhTqkxLCVr7WmHetwY0xFoDSw3xoAbPrDEGNPdWvtjFUY8osO9hiLGmMuAs4ABNhj7mPwANC/2/tGhxwLFGJOAK2ITrLWTfecphwxgiDHmTKA6UMcY8x9r7cWec8lhBLWeRVENC3TtCmjNUp3yJKj1pqQoqj8lBboeFRfQ2lSc9zqlfQzDzBjzHZBurd3iO0tZGGMGA48Cfay1Ob7zlIYxphpukvcAXBH7DBhhrc3yGqwMjPtr+CKwzVp7g+88FRU6w/X/rLVn+c4iFRekehakGhbk2hUNNUt1KjIFqd6UFKT6U1KQ61Fx0VCbivNVpzTHUIr8C6gNTDPGLDPGPO070JGEJnpfC3yMm2Q8MWiFDHd26HdA/9D3fVnoTJGIlE1galjAa5dqlsgvBab+lBTwelScalMY6IqhiIiIiIhIjNMVQxERERERkRinxlBERERERCTGqTEUERERERGJcWoMRUREREREYpwaQxERERERkRinxlBERERERCTGqTEUERERERGJcWoMJWoYY2YaY04PvX2fMeafvjOJiIDqk4hEJtUmKa6a7wAiYXQXcI8x5iigCzDEcx4RkSKqTyISiVSb5H+MtdZ3BpGwMcbMBmoBfa21u3znEREpovokIpFItUmKaCipRA1jTEegKfCTCpuIRBLVJxGJRKpNUpwaQ4kKxpimwATgHGC3MWaw50giIoDqk4hEJtUmKUmNoQSeMSYZmAz80Vq7ArgXN2ZeRMQr1ScRiUSqTXIommMoIiIiIiIS43TFUEREREREJMapMRQREREREYlxagxFRERERERinBpDERERERGRGKfGUEREREREJMapMRQREREREYlxagxFRERERERinBpDERERERGRGPf/ARbxd3LFm1c/AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "ax[0].set_ylabel(\"$P_X^{do(Y)}(x)$\")\n",
    "\n",
    "for i in range(3):\n",
    "    x, y = get_data(100000, 'normal', 'interventional', lambda x: 0, val_y = ybins[idx[i]])\n",
    "    sns.distplot(x, hist=False, kde=True, bins=600, color = colors[i], ax = ax[i])\n",
    "    ax[i].set_xlabel(\"$x$\")\n",
    "    ax[i].set_title(\"$do(Y = %.1f)$\" % ybins[idx[i]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EuCX42yPg54j"
   },
   "source": [
    "Intervention on $Y$ does not change the distribution of $X$, and $P_Y^{do(X=x)}(y) = P_{Y|X}(y|x)$. Consequently, we conclude $X \\rightarrow Y$, which supports our previous inference. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "lU_pgFMt4FOY"
   },
   "source": [
    "##### Causal Discovery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "12Ncy1BsuGTz",
    "outputId": "629a66c8-3869-4c82-cb14-6674d3453de3"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Step 1\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.1816308034723112 \n",
      "\n",
      "Step 2\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.7685187863147661 \n",
      "\n",
      "Step 3\n",
      "-> HSIC(x, r_y) p-value = 0.42927762050454266\n",
      "-> HSIC(y, r_x) p-value = 1.0 \n",
      "\n",
      "Step 4\n",
      "-> HSIC(x, r_y) p-value = 0.8376006856831653\n",
      "-> HSIC(y, r_x) p-value = 1.0 \n",
      "\n",
      "Step 5\n",
      "-> HSIC(x, r_y) p-value = 0.6071802951746832\n",
      "-> HSIC(y, r_x) p-value = 0.47058920183985475 \n",
      "\n",
      "Step 6\n",
      "-> HSIC(x, r_y) p-value = 0.6117110319388203\n",
      "-> HSIC(y, r_x) p-value = 0.39144278877755234 \n",
      "\n",
      "Step 7\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.6682980286501411 \n",
      "\n",
      "Step 8\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 1.0 \n",
      "\n",
      "Step 9\n",
      "-> HSIC(x, r_y) p-value = 0.2625786648753783\n",
      "-> HSIC(y, r_x) p-value = 0.4481284526387942 \n",
      "\n",
      "Step 10\n",
      "-> HSIC(x, r_y) p-value = 1.0\n",
      "-> HSIC(y, r_x) p-value = 0.7844030635679695 \n",
      "\n",
      "HSIC(x, r_y) p-value average =  0.774834829817659\n",
      "HSIC(y, r_x) p-value average =  0.671301112526139\n"
     ]
    }
   ],
   "source": [
    "p_x = []\n",
    "p_y = []\n",
    "\n",
    "for i in range(10):\n",
    "    print('Step', i+1)\n",
    "\n",
    "    x, y = get_data(200, 'normal', 't dist', lambda x: x, df = 20)\n",
    "    r_y = fit(np.expand_dims(x, axis=1), y)\n",
    "    r_x = fit(np.expand_dims(y, axis=1), x)\n",
    "    p_x.append(Hsic().test(x, r_y, workers = -1)[1])\n",
    "    p_y.append(Hsic().test(y, r_x, workers = -1)[1])\n",
    "\n",
    "    print('-> HSIC(x, r_y) p-value =', p_x[-1])\n",
    "    print('-> HSIC(y, r_x) p-value =', p_y[-1], '\\n')\n",
    "\n",
    "print('HSIC(x, r_y) p-value average = ', sum(p_x) / len(p_x))\n",
    "print('HSIC(y, r_x) p-value average = ', sum(p_y) / len(p_y))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Mwe00Qc8V33X"
   },
   "source": [
    "\n",
    "Independence is plausible in both directions, so we can not infer the causal direction. That is because the model is so close to the linear Gaussian model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "QvU2cX6p8TUO"
   },
   "source": [
    "### Old Faithful Geyser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "R2xlgCZfuGT2"
   },
   "outputs": [],
   "source": [
    "eruptions = []\n",
    "waitings = []\n",
    "\n",
    "with open ('./data/Old Faithful Geyser.txt' , 'r') as f:\n",
    "    lines = f.readlines()\n",
    "    for line in lines:\n",
    "        i, eruption, waiting = line.split()\n",
    "        eruptions.append(float(eruption))\n",
    "        waitings.append(float(waiting))\n",
    "        \n",
    "eruptions = np.array(eruptions)\n",
    "waitings = np.array(waitings)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "znP6JXhCSBJp"
   },
   "source": [
    "##### Plot Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 295
    },
    "id": "lUo-hANUSANG",
    "outputId": "247d9529-b97c-4958-c518-1f3416011532"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.xlabel(\"Eruptions\")\n",
    "plt.ylabel(\"Waitings\")\n",
    "plt.title(\"Waitings with respect to Eruptions\")\n",
    "_ = plt.scatter(eruptions, waitings, c = 'c', marker='*')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LhTM5Pp99DTk"
   },
   "source": [
    "##### Causal Discovery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "nCSWyv6PuGT5",
    "outputId": "251f0dcc-489a-4537-a9c5-b29effb2747d"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "HSIC(eruptions, r_waitings) p-value = 1.0\n",
      "HSIC(waitings, r_eruptions) p-value = 0.0005396209905119277\n"
     ]
    }
   ],
   "source": [
    "r_waitings = fit(np.expand_dims(eruptions, axis=1), waitings)\n",
    "r_eruptions = fit(np.expand_dims(waitings, axis=1), eruptions)\n",
    "\n",
    "print('HSIC(eruptions, r_waitings) p-value =', Hsic().test(eruptions, r_waitings, workers = -1)[1])\n",
    "print('HSIC(waitings, r_eruptions) p-value =', Hsic().test(waitings, r_eruptions, workers = -1)[1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "sQoP5g8QWkkD"
   },
   "source": [
    "$Eruption \\rightarrow Waiting$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kwhyS2w_dJ_r"
   },
   "source": [
    "### Tübingen Cause-Effect Pairs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "id": "OdYo5u2rhwR0"
   },
   "outputs": [],
   "source": [
    "def read_pair(index):\n",
    "    X = []\n",
    "    Y = []\n",
    "\n",
    "    with open ('./data/tuebingen/pair{}.txt'.format(index) , 'r') as f:\n",
    "        lines = f.readlines()\n",
    "        for line in lines:\n",
    "            x, y = line.split()\n",
    "            X.append(float(x))\n",
    "            Y.append(float(y))\n",
    "\n",
    "    xy = None\n",
    "\n",
    "    with open ('./data/tuebingen/pair{}_des.txt'.format(index) , 'r') as f:\n",
    "        lines = f.readlines()\n",
    "        for line in lines:\n",
    "            if 'x --> y' in line or 'x-->y' in line:\n",
    "                xy = True\n",
    "                break\n",
    "            if 'y --> x' in line or 'y-->x' in line:\n",
    "                xy = False\n",
    "            \n",
    "    return np.array(X), np.array(Y), xy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "42vWCm_PjARW"
   },
   "source": [
    "##### Causal Discovery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "hgHJMqppiYSy",
    "outputId": "c4b03997-f011-4a8d-91a8-e6be48630ea8"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "===> pair0001\n",
      "y --> x False \n",
      "\n",
      "===> pair0002\n",
      "x --> y True \n",
      "\n",
      "===> pair0003\n",
      "y --> x False \n",
      "\n",
      "===> pair0004\n",
      "y --> x False \n",
      "\n",
      "===> pair0005\n",
      "x --> y True \n",
      "\n",
      "===> pair0006\n",
      "y --> x False \n",
      "\n",
      "===> pair0007\n",
      "y --> x False \n",
      "\n",
      "===> pair0008\n",
      "y --> x False \n",
      "\n",
      "===> pair0009\n",
      "y --> x False \n",
      "\n",
      "===> pair0010\n",
      "y --> x False \n",
      "\n",
      "===> pair0011\n",
      "y --> x False \n",
      "\n",
      "===> pair0012\n",
      "y --> x False \n",
      "\n",
      "===> pair0013\n",
      "x --> y True \n",
      "\n",
      "===> pair0014\n",
      "y --> x False \n",
      "\n",
      "===> pair0015\n",
      "y --> x False \n",
      "\n",
      "===> pair0016\n",
      "x --> y True \n",
      "\n",
      "===> pair0017\n",
      "y --> x False \n",
      "\n",
      "===> pair0018\n",
      "x --> y True \n",
      "\n",
      "===> pair0019\n",
      "x --> y True \n",
      "\n",
      "===> pair0020\n",
      "y --> x False \n",
      "\n",
      "===> pair0021\n",
      "x --> y True \n",
      "\n",
      "===> pair0022\n",
      "x --> y True \n",
      "\n",
      "===> pair0023\n",
      "x --> y True \n",
      "\n",
      "===> pair0024\n",
      "x --> y True \n",
      "\n",
      "===> pair0025\n",
      "x --> y True \n",
      "\n",
      "===> pair0026\n",
      "y --> x False \n",
      "\n",
      "===> pair0027\n",
      "y --> x False \n",
      "\n",
      "===> pair0028\n",
      "x --> y True \n",
      "\n",
      "===> pair0029\n",
      "x --> y True \n",
      "\n",
      "===> pair0030\n",
      "y --> x False \n",
      "\n",
      "===> pair0031\n",
      "y --> x False \n",
      "\n",
      "===> pair0032\n",
      "x --> y True \n",
      "\n",
      "===> pair0033\n",
      "x --> y True \n",
      "\n",
      "===> pair0034\n",
      "x --> y True \n",
      "\n",
      "===> pair0035\n",
      "y --> x False \n",
      "\n",
      "===> pair0036\n",
      "x --> y True \n",
      "\n",
      "===> pair0037\n",
      "y --> x False \n",
      "\n",
      "===> pair0038\n",
      "x --> y True \n",
      "\n",
      "===> pair0039\n",
      "x --> y True \n",
      "\n",
      "===> pair0040\n",
      "x --> y True \n",
      "\n",
      "===> pair0041\n",
      "x --> y True \n",
      "\n",
      "===> pair0042\n",
      "x --> y True \n",
      "\n",
      "===> pair0043\n",
      "x --> y True \n",
      "\n",
      "===> pair0044\n",
      "x --> y True \n",
      "\n",
      "===> pair0045\n",
      "x --> y True \n",
      "\n",
      "===> pair0046\n",
      "y --> x False \n",
      "\n",
      "===> pair0047\n",
      "y --> x True \n",
      "\n",
      "===> pair0048\n",
      "y --> x True \n",
      "\n",
      "===> pair0049\n",
      "y --> x True \n",
      "\n"
     ]
    }
   ],
   "source": [
    "for i in range(1, 50):\n",
    "    index = str(i).zfill(4)\n",
    "    print('===> pair{}'.format(index))\n",
    "\n",
    "    x, y, xy = read_pair(index)\n",
    "    r_y = fit(np.expand_dims(x, axis = 1), y)\n",
    "    r_x = fit(np.expand_dims(y, axis = 1), x)\n",
    "    pval_x = Hsic().test(x, r_y, workers = -1)[1]\n",
    "    pval_y = Hsic().test(y, r_x, workers = -1)[1]\n",
    "\n",
    "    if pval_x < pval_y:\n",
    "        print('y --> x', not xy, '\\n')\n",
    "    else:\n",
    "        print('x --> y', xy, '\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "s7OV2l71e_Al"
   },
   "source": [
    "We examine a case in which our approach failed to reason correctly. In dataset $20$, $X$ causes $Y$; however, the exogenous noise is not independent of $X$, as you see in the following graph. This is in contrast with the method's assumption, and as a result, it fails. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 501
    },
    "id": "eARDSBLeYUwJ",
    "outputId": "f4b02d54-911e-4ea4-ef27-8ac115791c26"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light",
      "tags": []
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "index = str(20).zfill(4)\n",
    "x, y, ground_truth = read_pair(index)\n",
    "svr = SVR(kernel = 'rbf', C = 1000, gamma = 'auto', epsilon = 0.1, coef0 = 1)\n",
    "svr.fit(np.expand_dims(x, axis=1), y)\n",
    "\n",
    "plt.figure(figsize = (12, 8))\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.ylim(2, 10)\n",
    "plt.scatter(x, y, marker='o', s = 2, c = 'g')\n",
    "plt.plot(np.sort(x),svr.predict(np.expand_dims(np.sort(x),axis=1)), c='blue', linewidth=0.8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "-zBJ_AiyuLAn"
   },
   "source": [
    "## Graph Discovery"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "id": "Juj-kpC5uNXi"
   },
   "outputs": [],
   "source": [
    "X, Y, Z, W = [], [], [], []\n",
    "\n",
    "with open ('./data/TwoVarData.txt' , 'r') as f:\n",
    "    lines = f.readlines()\n",
    "    for line in lines[1:]:\n",
    "        i, x, y, z, w = line.split()\n",
    "        X.append(float(x))\n",
    "        Y.append(float(y))\n",
    "        Z.append(float(z))\n",
    "        W.append(float(w))\n",
    "\n",
    "x, y, z, w = np.array(X), np.array(Y), np.array(Z), np.array(W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "jIa_0MjBvMkl",
    "outputId": "f9048765-2616-45f5-f181-4cd4b529aeb9"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x --> y\n",
      "\n"
     ]
    }
   ],
   "source": [
    "r_y = fit(np.expand_dims(x, axis = 1), y)\n",
    "r_x = fit(np.expand_dims(y, axis = 1), x)\n",
    "pval_x = Hsic().test(x, r_y, workers = -1)[1]\n",
    "pval_y = Hsic().test(y, r_x, workers = -1)[1]\n",
    "\n",
    "if pval_x <= pval_y:\n",
    "    print('y --> x\\n')\n",
    "else:\n",
    "    print('x --> y\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "d4r2c84_wD0r",
    "outputId": "83b56c64-4e64-4903-b4cc-9132aec2e421"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y --> w\n",
      "\n"
     ]
    }
   ],
   "source": [
    "r_y = fit(np.expand_dims(w, axis = 1), y)\n",
    "r_w = fit(np.expand_dims(y, axis = 1), w)\n",
    "pval_w = Hsic().test(w, r_y, workers = -1)[1]\n",
    "pval_y = Hsic().test(y, r_w, workers = -1)[1]\n",
    "\n",
    "if pval_w <= pval_y:\n",
    "    print('y --> w\\n')\n",
    "else:\n",
    "    print('w --> y\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "HkQF-qYFvrwA",
    "outputId": "9ac387ae-8fb5-4641-f078-0663c720a698"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x --> w\n",
      "\n"
     ]
    }
   ],
   "source": [
    "r_x = fit(np.expand_dims(w, axis = 1), x)\n",
    "r_w = fit(np.expand_dims(x, axis = 1), w)\n",
    "pval_w = Hsic().test(w, r_x, workers = -1)[1]\n",
    "pval_x = Hsic().test(x, r_w, workers = -1)[1]\n",
    "\n",
    "if pval_w <= pval_x:\n",
    "    print('x --> w\\n')\n",
    "else:\n",
    "    print('w --> x\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "XKrpp1e3weH8",
    "outputId": "cd5ae3b9-3fb9-4572-956c-69e5b980fd7c"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "x --> z\n",
      "\n"
     ]
    }
   ],
   "source": [
    "r_x = fit(np.expand_dims(z, axis = 1), x)\n",
    "r_z = fit(np.expand_dims(x , axis = 1), z)\n",
    "pval_z = Hsic().test(z, r_x, workers = -1)[1]\n",
    "pval_x = Hsic().test(x, r_z, workers = -1)[1]\n",
    "\n",
    "if pval_z <= pval_x:\n",
    "    print('x --> z\\n')\n",
    "else:\n",
    "    print('z --> x\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "q-w8FPFMyz1M",
    "outputId": "b75a3275-ee05-449d-df54-edef4be523f1"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "y --> z\n",
      "\n"
     ]
    }
   ],
   "source": [
    "r_y = fit(np.expand_dims(z, axis = 1), y)\n",
    "r_z = fit(np.expand_dims(y , axis = 1), z)\n",
    "pval_z = Hsic().test(z, r_y, workers = -1)[1]\n",
    "pval_y = Hsic().test(y, r_z, workers = -1)[1]\n",
    "\n",
    "if pval_y <= pval_z:\n",
    "    print('z --> y\\n')\n",
    "else:\n",
    "    print('y --> z\\n')"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "PHW1.ipynb",
   "provenance": [],
   "toc_visible": true
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
